Physics 4C Spring 2016 Test 2

Size: px

Start display at page:

Download "Physics 4C Spring 2016 Test 2"

Alexis Gaines
5 years ago
Views:

1 Physics 4C Spring 2016 Test 2 Name: May 17, 2017 Please show your work! Answers are not complete without clear reasoning. When asked for an expression, you must give your answer in terms of the variables given in the question and/or fundamental constants. Answer as many questions as you can, in any order. Calculators are allowed. Books and notes are not allowed. Use any blank space to answer questions, but please make sure it is clear which question your answer refers to. The last question, question 4, is worth by far the most points. g = 9.8 ms 2 P 0 = Pa = 1 atm R = J mol 1 K 1 k B = J/K N A = m p = kg σ = W m 2 K 4 1 cal = J 1 ev = J Fahrenheit to Celsius: ([ F] 32) 1.8 =[ C] Celsius to Fahrenheit: ([ C] 1.8) + 32 =[ F] e = 1 1 (V 1 /V 2 ) (γ 1) v+dv v N v dv = v+dv v ( ) 3/2 m 4πN 0 2πk B T v 2 e m 0v 2 /2k B T dv 1

2 below it. Atmospheric pres an expression for the angle of bending u as a function is P 0. We wish to find the h of the initial length of the strips, their average coefficients of linear expansion, the change in temperature, h in Figure P (a) W analysis model is appropria 1. The rectangular and platethe shown separation has anof area the Acenters i equal to of lw. the strips For this (Dr plate 5 α is the describe average the piston? (b) W coefficient of linear r 2 2 expansion. r 1 ). (b) Show that the angle of bending decreases an appropriate force equa to zero when DT decreases to zero and also when the for the piston from this a two average coefficients of expansion become equal. (a) If the temperature increases by T, show that the increase in areasis ismodel A = in terms of P, P (c) What If? What happens if the strip is cooled? 2αA i T. [5 pts] A, and g. (c) Suppose n mol 61. The rectangular plate shown in Figure P19.61 has an an ideal gas are in the cyli (b) What approximation Q/C area A i equal does to,w. thisif expression the temperature assume? increases [1 pt] by DT, Substitute for P in your an height h of the piston above w T i w w Figure P19.61 TT i T 65. Review. Consider an ob Q/C shapes displayed in Table 1 increase in the moment of it is warmed from 08C to (a) copper or (b) aluminu ear expansion coefficients vary between 08C and 1008 for parts (a) and (b) the sa 2

3 2. A copper calorimeter with a mass of 250 g contains 500 g of water. The calorimeter and water are in thermal equilibrium at 15.0 C. A metallic block is placed into the water, which has a mass of g and is originally at a temperature of 125 C. The entire system stabilizes at a final temperature of 20.0 C. The specific heat of copper is 387 J kg 1 C 1. Determine the specific heat of the unknown sample. [6 pts] 3

4 3. Consider a gas of identical molecules, each with mass m 0, in thermal equilibrium at temperature, T. (a) Sketch the distribution of molecular speeds and label the most probable speed for a gas molecule on it. [4 pts] (b) Starting from the Maxwell-Boltzmann speed distribution, find an expression for the most probable speed of a gas molecule. [5 pts] (c) What is the the root-mean-square (rms) speed for the gas and how does the rms speed relate to the most probable speed? [2 pts] 4

5 4. A sample of a diatomic ideal gas with specific heat ratio 1.40, confined to a cylinder, is carried through a closed cycle. The gas is initially at pressure P 0 and volume V 0. First, in step 1, its pressure is tripled under constant volume. Then, in step 2, it expands adiabatically to its original pressure. Finally, in step 3, the gas is compressed isobarically to its original volume. (a) Draw a PV diagram of this cycle, labeling the steps. [4 pts] (b) Find an expression for the volume of the gas at the end of the adiabatic expansion in terms of V 0. [3 pts] (c) Assuming that there are n moles of gas in the sample, find expressions for the temperatures of the gas at the start of the adiabatic expansion, at the end of the expansion, and at the end of the cycle. [4 pts] (d) During which of the three steps does heat enter the gas? During which of the three steps does heat leave the gas? [2 pts] (e) If the cycle is used as a heat engine, what is the engine s efficiency? numerical value.) [7 pts] (Find a (f) How does that compare to the efficiency of a Carnot engine operating between the same temperature extremes? (Find the Carnot engine s efficiency.) [3 pts] 5

6 Extra Workspace 6

7 Extra Workspace 7

Dual Program Level 1 Physics Course

Dual Program Level 1 Physics Course Assignment 15 Due: 11/Feb/2012 14:00 Assume that water has a constant specific heat capacity of 4190 J/kg K at all temperatures between its melting point and boiling