Week 1 Temperature, Heat and the First Law of Thermodynamics. (Ch. 19 of Serway&J.) (Syllabus) Temperature Thermal Expansion Temperature and Heat Heat and Work The first Law Heat Transfer
Temperature Thermodynamics: the study of thermal energy (or internal energy) of systems. Temperature: a directly measurable property of matter related to its internal energy, U, or Eint. The bigger T, the bigger U. But U can increase while T stays fixed. Temperature: a measure of the mean kinetic energy per particle in matter. Ex.) monotonic gas ½ mvrms2 = 3/2 kt
Temperature... is fairly intuitive, except that our sense of hot and cold can be wrong: two objects at the same temperature but different compositions may feel unequal in temperature. Thermal conductivity makes a difference in how hot or cold an object feels. So does our own skin's temperature. What we really feel is heat transfer. Real thermometers are not fooled so easily. But they must be given time to reach thermal equilibrium with the object of interest.
Temperature The zeroth law of thermodynamics. When two bodies are in thermal equilibrium, they have the same temperature.
Temperature Measurement Electronic thermometer - electrical resistance Mercury thermometer - volume expansion Bimetallic strip thermometer - linear expansion Constant-volume gas thermometer - Pressure T
Temperature Scale Definitions We use the triple point of water to define temperature scales (especially Celsius). Triple point of water = 273.16 K Triple point of water: the temp and pressure when the solid, liquid and gas phases are in equilibrium.
Temperature Scale Definitions (cont.) Comparison of 3 scales: o o Boiling Pt. 100 C 212 F 373 K Freezing Pt. 0 oc 32 of 273 K Τ 100 180 100 Which unit is the smallest? Conversion Equations Examples: TF = 1.8 TC + 32 TF = 1.8 TK + 459
Temperature Concept Questions: 1. Which of these scales has the largest units? 2. Find a conversion from TR to TS. 3. At what temperature is TR = TS? (Also try Checkpoint 1, p. 430.)
Thermal Expansion Objects increase in length, area, and volume with temperature. (Exception: water near freezing.) Different materials expand by different fractional amounts. (See Table 19.1) L= L T Pyrex =3.2x10 6, Al =23x10 6 per oc
Thermal Expansion Area Expansion A=A T =2 Volume Expansion V =V T =3 Q: will a hole become larger or smaller? Demo: have people stand in line and then form a ring... Demo: ball and ring wands.
An Ideal Gas For gases, the interatomic forces within the gas are very weak We can imagine these forces to be nonexistent Note that there is no equilibrium separation for the atoms Thus, no standard volume at a given temperature
Ideal Gas, cont For a gas, the volume is entirely determined by the container holding the gas Equations involving gases will contain the volume, V, as a variable This is instead of focusing on V
Gas: Equation of State It is useful to know how the volume, pressure and temperature of the gas of mass m are related The equation that interrelates these quantities is called the equation of state These are generally quite complicated If the gas is maintained at a low pressure, the equation of state becomes much easier This type of a low density gas is commonly referred to as an ideal gas
Ideal Gas Model The ideal gas model can be used to make predictions about the behavior of gases If the gases are at low pressures, this model adequately describes the behavior of real gases
The Mole The amount of gas in a given volume is conveniently expressed in terms of the number of moles One mole of any substance is that amount of the substance that contains Avogadro s number of constituent particles Avogadro s number NA = 6.022 x 1023 The constituent particles can be atoms or molecules
Moles, cont The number of moles can be determined from the mass of the substance: n = m /M M is the molar mass of the substance Can be obtained from the periodic table Is the atomic mass expressed in grams/mole Example: He has mass of 4.00 u so M = 4.00 g/ mol m is the mass of the sample n is the number of moles
Gas Laws When a gas is kept at a constant temperature, its pressure is inversely proportional to its volume (Boyle s law) When a gas is kept at a constant pressure, its volume is directly proportional to its temperature (Charles and Gay-Lussac s law) When the volume of the gas is kept constant, the pressure is directly proportional to the temperature (Guy-Lussac s law)
Ideal Gas Law The equation of state for an ideal gas combines and summarizes the other gas laws PV = nrt This is known as the ideal gas law R is a constant, called the Universal Gas Constant R = 8.314 J/mol K = 0.08214 L atm/mol K From this, you can determine that 1 mole of any gas at atmospheric pressure and at 0o C is 22.4 L
Ideal Gas Law, cont The ideal gas law is often expressed in terms of the total number of molecules, N, present in the sample PV = nrt = (N/NA) RT = NkBT kb is Boltzmann s constant kb = 1.38 x 10-23 J/K It is common to call P, V, and T the thermodynamic variables of an ideal gas If the equation of state is known, one of the variables can always be expressed as some function of the other two
Temperature and Heat Heat is the energy that is transferred between a system and its environment because of a temperature difference that exists between them. Q = heat added to system Units: Joule, calorie, Btu, erg, kilocalorie
Absorption of heat by solids and liquids Heat capacity Q= C T Specific Heat Q= cm T c for aluminum is 900 J/(kg K) c for water is 4186 J/(kg K) or 1 cal/(g K) Heats of Transformation (melting/freezing or boiling/ condensation) Q= LF m Q= LV m
Heat and Work - gases d dw =F s Let W = work done by a gas. dw = pa ds = p A ds = p dv Vf Vf W = dw = p dv Vi Vi
Heat and Work in gases p-v diagrams Vf Vf W = dw = p dv Vi Vi
Heat and Work - gases Checkpoint 4. The p-v diagram here shows six curved paths (connected by vertical paths) that can be followed by a gas. Which two of them should be part of a closed cycle if the net work done by the gas is to be at its maximum positive value?
1st Law of thermodynamics Eint =Eint,f Eint,i Eint =Q W This version applies to gas systems. st 1 law (most generally) is conservation of energy Recall cons. of mechanical energy: E = K + U mech In both versions, if the system is closed, E = 0. E is path independent. int Checkpoint 5 Rank the paths according to a) Eint, (b) W done by gas, c) magnitude of Q, greatest first.
Special Processes for gas systems 1. 2. 3. 4. Adiabatic. Q=0. Constant-volume. V = 0. Cyclical. Eint=0. Free-expansion. W=Q=0 Eint=-W Eint=Q Q=W. Eint=0 5. Isothermal. Τ = 0 6. Constant volume V = 0. (repeat) 7. Constant pressure p = 0