P V T 1 P 1 V 1 T 1. Question 3 : Find the efficiency of the triangular cycle.

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1 hys Midterm H. Beker Spring '79 Question : Question : A uniform rod is bent into a rectangle. Two diagonal corners are held at º C and º C. Find the temperatures of the other two corners. º C L L L L º C hys Midterm H. Beker Spring '79 Question : One mole of polyatomic gas is taken through the cycle shown. Copy the following table to your answer sheet and fill in the blanks using only,, T. adiabatic T T 8 hys Midterm H. Beker Spring '79 Question : Find the efficiency of the triangular cycle. T T hys Midterm H. Beker Spring '79 Question 4 : One mole of an ideal gas takes 7 R T amount of heat on the path shown. Find the degrees of freedom. T S hys Midterm H. Beker Spring '79 Question 5 : One mole of an ideal monatomic gas goes from point to point as shown. Find Q, W, U, S. hys Midterm H. Beker Spring '79 Question 6 : Two chambers of volumes,and, are enclosed in a rigid insulating material. µ moles of gas initially kept in by a closed stopcock. The gas freely expands after the stopcock is opened. Find the change of entropy in terms of µ, R,,. hys Midterm H. Beker Spring '79 Question : A block is on a piston which is moving vertically with a simple harmonic motion of period π seconds. At what amplitude of motion will the block and piston separate?

2 hys Midterm H. Beker Spring '79 Question : Fill in the blanks, T isothermal 4 hys Midterm H. Beker Spring '79 Question : Fill in the blanks, Q W U isothermal T adiabatic adiabatic 4 hys Midterm H. Beker Spring '79 Question : Fill in the blanks, isothermal S 4 4 Total adiabatic 4 hys Midterm H. Beker Spring '8 Question : Find the ω of the system. k =N/m k =6N/m k =8N/m k k m k hys Midterm H. Beker Spring '8 Question : A U-tube is filled with a liquid. Find the ω of the oscillations of liquid columns, if the length of the liquid in the u-tube is L. L hys Midterm H. Beker Spring '8 Question : Standing waves are formed on a m long wire. The wire has a mass of 4 grams and is under tension as shown: a) Find the wave velocity on the string. b) Find the wavelength of the fundamental vibration. c) What are the two lowest frequencies produced? m =.5 kg m

3 hys Midterm H. Beker Spring '8 Question 4 : S emits sound with frequency 5 sec. What is the frequency heard by D. elocity of sound is m/sec. S m/s 6 m/s D hys Midterm H. Beker Spring '8 Question : Two concentric spherical shells are held at temperature C and 6 c respectively, as shown. Find the temperature at r = R/, half way between the shells. The heat flows is at steady state. hys Midterm H. Beker Spring '8 T Question : A polyatomic gas goes through the reversible cycle shown. Copy and complete T dt= dq= the table on your answer sheet, showing all /8 calculations. d= /8 hys Midterm H. Beker Spring '8 Question : Copy and complete the table on U Q W S your answer sheet, for one mole of a - dt= polyatomic gas in cycle shown. What is - dq= efficiency of the cycle? - d= Total /8 hys Midterm H. Beker Spring '8 Question 4 : gr of ice at - C is heated so that it melts and its temperature rises to 7 C. The specific heat of ice is.5 cal/gr- K and that of water is cal/gr- K, while 8 cal/gr is needed to melt the ice. Find the total entropy change of the system due to the heating process hys Midterm H. Beker Spring '9 Question : Calculate the minimum length for a pipe that has a fundamental frequency of 4 Hz, if the pipe is a) closed at one end, b) open at both ends (speed of sound = m/s ) hys Midterm H. Beker Spring '9 Question : n moles of an ideal diatomic gas doubles its volume from to by a process in which is proportional to (see figure ). Calculate: a) The final pressure. b) The final temperature, c) W d) U e) Q (Express your answer in terms of n, R, and ) 6 C C r=/ R R R T(/ R) =?

4 hys Midterm H. Beker Spring '9 Question : n moles of an ideal gas is taken along the right triangular cycle shown in the -T diagram figure. Calculate the net work done per cycle in terms of n, R and T 4 T T T hys Midterm H. Beker Spring '9 Question 4 : For one mole of monatomic ideal gas consider the cycle shown in figure. rocess ab is heating at constant volume, bc is adiabatic and ca is isothermal at temperature T. Given that Q ab = (9/)RT, calculate : a) T b b a b) W bc c) a / c c d) Q ca (Express your answer in terms of R and T ) hys Midterm H. Beker Fall '94 Question : A source and an observer approach each other with relative velocity m/s. The source emits a sound of frequency 5 Hz, while the observer hears 55 Hz. Find the velocities of the source and the observer. S v s v o sound = m/s O hys Midterm H. Beker Fall '94 Question : Two liquids that do not mix and a block are in a cup as shown in figure. What portion of the block is in the denser fluid? hys Midterm H. Beker Fall '94 Question : When a gas is heated from temperature T to T+6 degrees, the average velocity of its molecules increase by %. Calculate T. hys Midterm H. Beker Fall '94 Question 4 : One mole of gas is taken through a cycle as shown in figure. Copy the below table to your answer sheet and fill in the blanks in terms of R, c v,,. U Q W adiabatic / L ρ ρ ρ x ρ >ρ >ρ Straight line hys Midterm H. Beker Fall ' Question : An irregular shaped solid weighs 64 N in the open but 5 N when submerged in water. ( g = m / sec ) a) What is its volume in liters? b) What is its density?

5 hys Midterm H. Beker Fall ' 5 Question : The force of interaction between the two atoms of a diatomic molecule is given by : A B f = +. (A, B > ) Calculate k, the spring constant for small oscillations around equilibrium. 4 r r hys Midterm H. Beker Fall ' Question : A standing wave of amplitude A, in the fundamental ( n = ) mode is formed on a string with linear mass density µ, under tension T, stretched between x = and x = L. Calculate the total energy. hys Midterm H. Beker Fall ' Question 4 : A car emitting sound of frequency Hz approaches a wall with /6 of the speed of sound. Calculate the frequency of the sound reflected from the wall, as observed by a person in the car. hys Midterm H. Beker Fall '6 dq J Question : A steel of kg, heat capacity c = = 5, at temperature 7 o C is brought into contact m dt kg C with a similar (same c) block of kg at temperature 57 o C. ( k= o C + 7 ) a) Final temperature (in K) =? b) S for the cold block =? c) S for the hot block =? d) Overall S =? hys Midterm H. Beker Fall '6 Question : moles of an ideal gas with γ =,5 is taken through the cycle shown. Calculate c v using R =5/ (J/mole K). Copy the table to your answer sheet and fill in the blanks. (simplified numerical answers!) T dq= dt= d= hys Midterm H. Beker Fall '6 E Q W Question : moles of an ideal gas with dt= γ =,5 is taken through the cycle shown. Copy the table to your answer sheet and fill in the d= blanks. Then calculate the efficiency of the dq= heat engine. (simplified numerical answers!) hys Midterm H. Beker Fall '6 Question 4 : Block M is initially at rest when a bullet of mass m, speed v embeds in M. Calculate: a) period oscillations, b) amplitude of oscillations. M µ= k

6 hys Midterm E. Arık Spring '7 6 Question : A monatomic ideal gas initially at i, i, and T i is taken through a cycle as in the figure. a) Calculate the change of internal energy for the process A B? b) Find the net work done by the gas per cycle. c) What is the net energy added by heat to the system per cycle? hys Midterm E. Arık Spring '7 Question : A diatomic ideal gas confined to a cylinder is put through a closed cycle. Initially the gas is at i, i, and T i. First, its pressure is doubled under constant volume. It then expands adiabatically to its original pressure and finally is compressed isobarically to its original volume. a) Draw a diagram of this cycle. b) Determine the volume at the end of the adiabatic expansion. c) Find the work done by the gas during the adiabatic expansion hys Midterm E. Arık Spring '7 Question : Standing at a crosswalk, you hear a frequency of 56 Hz from the siren of an approaching ambulance. After the ambulance passes, the observed frequency of the siren is 48 Hz. Determine the ambulance s speed from these observations (take the speed of sound as 4 m/s). hys Midterm E. Arık Spring '7 Question 4 : A standing-wave pattern is observed in a thin wire with a length of. m. The equation of the wave is y = (. m) sin(πx) cos(πt) where x is in meters and t is in seconds. a) How many loops does this pattern exhibit and what is the frequency of vibration of the wire? b) What is the fundamental frequency of vibration of the wire? c) If the original frequency is held constant and the tension in the wire is increased by a factor of 9, how many loops are present in the new pattern? hys Midterm M. Mungan SRING 8 Q H Question : A diesel engine undergoes a - cycle as shown in the B C adiabatic figure. Assume that the gas is diatomic, γ = 7/5. Copy the point table shown into your answer sheet and complete it. D OINT T A B T C D B C A Question : For the Diesel engine of problem ), copy the path table shown below into your answer sheet and complete it. ATH E Q W A B B C C D D A A Q C

7 7 hys Midterm N. Inci SRING 8 π Question : A string vibrates according to equation y = 4 sin x cos( π t ), where x and y are in metres and t is in seconds. a) What are the amplitude and speed of the component waves whose superposition can give rise to this vibration? b) Find the distance between the nodes. c) What is the velocity of a particle of the string at the position x= m at time t=/ s. Do not forget the indicate the physical units in your answer. Amplitude of the component waves Speed of the component waves Distance between the nodes article velocity at x= m, t=/ s hys Midterm N. Inci SRING 8 Question : A sound wave of wavelength λ propagates in a D-shape tube and its intensity splits into two parts at the first joint of the tube. One part follows the bent arm of r and the other part follows the r straight path, as shown in the Figure. They interfere at the detector. What must be the smallest radius r such that a minimum will be heard at the detector? source detector hys Midterm N. Inci SRING 8 D Question : A thin cylindrical metal pipe is carrying steam at temperature T s. The pipe has a diameter of a and is wrapped with a thickness b-a of fibre glass insulation. A length D of the pipe passes through a room in which the temperature is T R. How much heat is lost through the insulation. insulator hys Midterm N. Inci SRING 8 C C Question 4: How much work is required to compress one mole of air Adiabatic (γ=c p /c v =) at T and to one half the original volume a) by an isothermal process? b) how much work is required to produce the same compression in an B B Isothermal adiabatic process? c) Determine B, C, T B and T C. All results should be A expressed in terms of T, and R. T A T W B A B C A C hys Midterm DEMIRAL, ERCAN, KAYA SRING 8 Question : A wave is given by y=5 Sin(x+5t+), where all values are in mks units.find a) the amplitude, b) the wavelength, c) the frequency, d) the wave velocity vector, the phase constant b a T R T s

8 hys Midterm DEMIRAL, ERCAN, KAYA SRING 8 8 Question : DERIE the frequency observed by an observer moving towards a stationary sound source with a speed U. Take the speed of sound to be s and the frequency of the source to be f. (Show all your steps) hys Midterm DEMIRAL, ERCAN, KAYA SRING 8 y Question : Two identical loud speakers S and S, separated by a distance of d=λ, emit waves of wavelength λ. Find the positions of minimal intensity along the y axis. (S and S are in phase). S S d=λ hys Midterm DEMIRAL, ERCAN, KAYA SRING 8 Question 4: In a Young's interference experiment, the two slits are separated by.5 mm and the incident light includes two wavelengths: λ =54 nm (green) and λ =45 nm (blue). The overlapping interference patterns are observed on a screen.4 m from the slits. Calculate the minimum distance from the center of the screen to a point where bright fringe of the green light coincides with a bright fringe of the blue light. hys Midterm N. Ercan FALL 8 Question : If the wave function is given by y=.sin(x-4t) in SI units, find; a) Frequency, b) the wavelength, c) the velocity, d) angular frequency, e) the wave number of the wave, f) if the mass density of the string on which the wave propagates is.5 kg/m, what is the transmitted power? hys Midterm N. Ercan FALL 8 Question : Write down the equation of a wave, travelling along +x axis with an amplitude of. m, a frequency of 44 hz, and a speed of m/sec. hys Midterm N. Ercan FALL 8 Question : For the wave described by y=.5sin(π/6 (x-64t)) in SI units, determine The first positive x coordinate where y is a maximum when t=, x coordinate of the second maximum when t=, maximum transverse speed of the particles of the medium. hys Midterm N. Ercan FALL 8 Question 4: A harmonic longitudinal wave propagating down a tube filled with a compressible gas has the form S(x,t)=SmCos(kx-ωt). What is its velocity? hys Midterm N. Ercan FALL 8 Question 5: While you are sounding a tone on a toy whistle, you notice a friend running towards you. If you want her to hear the same frequency that you hear even thoug she is approaching, what you must do? hys Midterm N. Ercan FALL 8 Question 6: Two harmonic waves traveling in a opposite directions interfere to produce a standing wave described by y=sin(4x)cos(t) where x is in m and t is in sec. What is the speed (in m/s) of the interfering waves? x

9 hys Midterm N. Ercan FALL 8 9 Question 7: Two instruments produce a beat frequency of 5 hz. If one has a frequency of 64 hz, what could be the frequency of the other instrument? hys Midterm N. Ercan FALL 8 Question 8: Two of moles of an ideal gas are placed in a container of adjustable volume. When measurements are made, Ahmet says: a) the pressure is inversely proportional to the volume at constant temperature; Ayşe says: b) The temperature is directly proportional to the pressure at constant volume? Who is giving the correct answer? hys Midterm N. Ercan FALL 8 Question 9: Ideal gas in a container increases its pressure from atm. to atm. while keeping its volume constant. How much work is done (in Joules) by the gas if the volume is 5 liters? hys Midterm A. Sevgen FALL 8 Question 4: Write the harmonic of an oscillating string of length L, mass density µ, and tension T, shown in the figure Ψ(x,t)=sinkx cos kυt, that is, find k L explicitly. Which harmonic is this mode? hys Midterm Y. Skarlatos FALL 8 Question : Two identical sinusoidal waves with same frequency and amplitude but differing in phase travel in the same direction with the same speed. Determine the phase difference between the two waves if the resultant wave is to have the same amplitude as that of each of the initial two. Hint: Using phasors might be simpler than trigonometric methods. hys Midterm Y. Skarlatos FALL 8 Question : Two antennas are meters apart, and emit equal amplitude and phase electromagnetic waves with a wavelength of meters. Each antenna m emitting alone sends waves of intensity I at the source. A receiver at oint A is 4 meters directly in front of one of the antennas. What is the resultant 4m intensity at A when both antennas are emitting. hys Midterm N. Đnci Spring '9 A Question : Gas within a chamber undergoes the processes shown in the p diagram. Calculate the net heat added to the system during one complete cycle. bc curve has a characteristics of p = α, where α 6 7 p =

10 hys Midterm N. Đnci Spring '9 Question : A metal sphere of radius a is kept at temperature T. It is surrounded with a spherical fiber-glass shell of thermal conductivity κ and thickness a, which is concentric with the sphere. The temperature at the outer surface of the shell is measured to be T/. How much heat is lost through the insulation? T [Hint: H = κ A ]. α 6 x 7 p = hys Midterm N. Đnci Spring '9 Question : Speed of sound in air is v. A student uses an audio oscillator of adjustable frequency to measure the depth of a water well L. He reports hearing two successive resonances at f and at (6/5)f. (a) Determine the depth of nv v the well in terms of v and f. (b) Calculate L. Hint: ν n = ; ν n = n + L L hys Midterm N. Đnci Spring '9 Question 4 : Two sources are located m apart and are producing the following waves: y = Asin( kx ωt), y = Asin( k( x ) + ωt + π ) Find all x such that minima occur, in terms of wavelength λ. hys Midterm M. Mungan, A. Ankay Spring 9 Question : An isolated system consists out of N diatomic particles of an ideal gas in a cylindrical container with a movable piston on its top. The cylinder has cross sectional area A and the piston has mass m. Initially the volume of the gas is and apart from the weight of the piston there is no other source of pressure on the gas. It is observed that when heat is supplied to the system the piston rises. Assume that heat is added very slowly to the system. a) What type of process is this? b) What amount of heat Q has to be supplied to the system so that the piston rises by a height h? hys Midterm M. Mungan, A. Ankay Spring 9 Question : One mol of a monatomic ideal gas undergoes the following -point cycle : * At state the gas has pressure and volume. * An isothermal expansion brings it to the point where it has volume * State is reached by a constant volume process. * The process from back to state is adiabatic. a) Draw the - diagram of this cycle. b) Copy the path table given below to your answer sheet and complete it. State all your answers in terms of R, and. ath Tables ath E Q W c) In the - diagram of part(a) clearly indicate the process where heat flows in or out of the system and mark the direction with an arrow. d) Calculate the efficiency η E of the engine.

11 hys Midterm M. Mungan, A. Ankay Spring 9 Question : A small cube of water of mass m at temperature slightly above the freezing point T f is put into the freezer section of a refrigerator. a) It is observed that a net amount of heat Q is transferred to the freezer. Assuming that the freezer operates at a constant temperature, what is the temperature T of the freezer unit? b) Calculate the entropy change for he cube of water. c) Did the entropy found in part(b) increase or decrease? Does this violate the second law of Thermodynamics? Explain your answer. hys Midterm M. Arık Fall π π Question 4 : A travelling wave on a string lying on x-axis is given by y = sin( πx + ) in SI units. 4 a. Find the amplitude, wavelength, frequency and period of this wave. b. What is the wave velocity? In which direction does the wave travel? c. lot the wave at t= and at t=s on same graph. hys Midterm A. Ankay Spring Question : Two concentric spheres have radii r and R ( R > r ). The surface temperatures of the spheres are fixed at T r and T R ( T r > T R ) and the medium filling the region between the two surfaces as a constant thermal conductivity of α. Find the steady state heat flow rate radially outward from the inner surface to the outer one. hys E. Demiralp Midterm Spring ' Question : For a sound wave in a gas, the displacement of the vibrating particles of x the medium for their rest positions is given by the wave function: y( x, t) = Acos( t) where all quantities are in SI units. a) Find the wavelength, the frequency and the speed of the sound wave in the gas. b) Show that y(x; t) is a solution of the linear wave equation. hys E. Demiralp Midterm Spring ' Question : A string both ends fixed on a musical instrument vibrates to produce its natural frequencies. The length of the string is L =.4 m. By taking one end at x =, the other end x = L and calculating wavelengths and frequencies,.4m x= x=l a) write an explicit form of the wave function y(x; t) of the standing wave for the fundamental frequency f of the vibrations, b)by drawing roughly the wave function y(x; t) corresponding to the second harmonic with the frequency f, show the nodes and antinodes for this standing wave. Take the speed of wave on the string v = 6 m/s and the amplitude for the vibration at an antinode.x m

12 hys E. Demiralp Midterm Spring ' y Question : Two identical loud speakers S and S, separated by a distance of d = λ emit waves with a wavelength of λ. Find the positions of minimal intensity (destructive interference) along the y axis. (S and S are in phase). hys Midterm E. Demiralp Spring ' Question 4: An ideal gas system initially has the volume and the pressure. It is taken to a final state with the volume and the pressure along the curve =constant on the - diagram. During this process, 4 kj of heat also flows into the system. Initially, the internal energy of the gas is given as E. Calculate the internal energy of the final state. hys Midterm M. Sheftel Fall Question : The working substance is an engine, that undergoes a cycle given below, n is moles of ideal gas with a given γ. a. Draw the cycle on a - diagram, b. Copy the oint Table shown below into your answer sheet and complete it using only the given,, T, k >, γ >. oint Table OINT T T k hys Midterm B. Ünlü Fall ' Question : (a) Show that the function y(x,t) = sin(x)cos(vt) is a solution to the wave equation. (b) Show that the function in part (a) can be written as f(x+vt) = g(x-vt) and determine the functional forms for f and g. (Hint: sin(a±b) = sin(a)cos(b) ± cos(a)sin(b) ) hys Midterm B. Ünlü Fall ' Question : Give the derivation of the Doppler-shift expressions for the following cases, a) source is at rest and observer is moving away from the source with a constant velocity, b) observer is at rest and source is moving toward the observer with a constant velocity. hys Midterm B. Ünlü Fall ' Question : Two strings in the figure are of equal length and are being driven at equal frequencies. The mass per unit length of the left string is g/m. What is the mass per unit length of the right string? Streched spring S d = λ S x

13 hys Midterm B. Ünlü Fall ' Question 4 : A uniform rectangular plate of length l and width ω has a coefficient of linear expansion α. If the temperature is increased by T, calculate the change in the area ( A) of the plate in terms of α,l, ω and T. (Hint: Neglect very small quantities.) ω + ω l + l hys Midterm N. Ercan Spring ' Question : (Note that point C is fixed.) The strings are under a tension of T. (a) How long will it take for a wave pulse moving in the +x direction to travel from point A to point C? (b) How long will it take for the reflected wave pulse from B to return to point A? Indicate the orientation of this reflected pulse relative to the original pulse. A B C L L hys Midterm N. Ercan Spring ' Question : In a radar speed detection system, a stationary police car sends out radar waves of frequency f and these waves are traveling at speed c. The wave is reflected by a moving car and the reflected wave is detected by the police radars system. Let the car be approaching the police car at v, and (since this is very small compared to the speed of light) use the formulas for sound waves. a. Find the frequency f which is the radar frequency reflected by the moving car. b. Find the frequency f which is the radar frequency received back by the police car. c. What is the beat frequency? (Hint: Beat is the difference between ongoing and incoming frequencies to police car). hys Midterm N. Ercan Spring ' Question : A loud speaker is mounted at the same height as the ears of a listener and aimed at a wall as shown, sending beam of sound waves toward the wall. The listener starts from the wall and walks slowly toward the speaker. The x speaker emits sound of wavelength λ=.8d. At a certain time the listener is at distance x < d from the wall. (a) What is the phase difference (in radians) between the wave received by the listener directly from the speaker and the wave received after it is reflected from the wall (There is no phase change in the waves d on reflection from the wall). Give the answer in terms of x and d. (b) For what values of x ( d) will the listener hear maximum intensity? hys Midterm N.Ercan Spring ' Question 4: A liquid with a coefficient of volume expansion β just fills a spherical shell of volume. The shell is made of a material that has an average coefficient of linear expansion α. The liquid is free to expand into an open A h capillary of area A projecting from the top of the sphere. If the temperature increases by T, find the amount h that the liquid rises in the capillary in terms of given quantities (Neglect the expansion of capillary). T T + T hys Midterm M. Arık Spring ) ( pt ) a) State the principle of equipartition of energy. ( pt ) b) Explain why a monatomic gas always has C v =R/. ( pt ) c) Explain why a diatomic gas may have C v =R/, C v =5R/ or C v =7R/ depending on temperature.

14 4 hys Midterm M. Arık Spring ) The ratio of specific heats for the ideal gas in this problem is γ=. The gas goes through the cycle shown in figure. AB is isobaric, BC is adiabatic, CA is isothermal. ( pt ) a) Find the pressure and volume at point C in terms of o and o. ( pt ) b) Calculate C v and C p in terms of R. ( pt ) c) Make a table showing E, Q and W for the three processes AB, BC and CA. ( pt ) d) Calculate the efficiency of this heat engine and compare it with the efficiency of a Carnot cycle operating between the hottest and coolest temperatures in this cycle. A B (Bonus pt ) e) State a reason why the ratio of specific heats for this ideal gas may be. hys Midterm M. Arık Spring 4) For the process shown in above figure calculate the entropy change for n moles of gas (use ln =.7) ( pt ) a) for the process BC, ( pt ) b) for the process CA, ( pt ) c) for the process AB. hys Midterm?? Fall o o o C