Test 2 Review
Ideal Gas—PV=nRT—Watch units
W=PV; work done by gas vs. on gas
Adiabatic, isothermal, constant V, and P
Thermal equilibrium—Entropy
Heat --Internal energy—kinetic vs. T
1st and 2nd laws of thermodynamics
U = Q + W (Won gas=+; Wdone by gas= -)
Heat transfer: Q=mcT
Phase change: Q=mL
Radiation, convection, conduction
Multiple choice practice
1. A container holds 1mol of an ideal gas. 500J of heat are added to the gas. The temperature increases most
(a) if the volume is held constant.
(b) if the pressure is held constant.
(c) Both (a) and (b) give the same increase in temperature.
(d) There is insufficient information given to make a determination.
2. A pipe organ is manufactured near sea level with barometric pressure of P=760torr. It is then transported to a region well above sea level with a barometric pressure of P=670torr. Assuming the organ is housed in a room at the same temperature, the frequency of individual pipes will be
(a) less than before
(b) greater than before
(c) the same as before
HINT: Recall that the speed of sound in air is and the frequency is (or if a closed pipe).
Two identical containers hold equal amounts of the same gas at the same temperature. In each case, a piston compresses the gas to half the original volume. In one container the process takes place adiabatically, and in the other container it takes place at constant temperature in contact with a heat reservoir. The piston must do more work in the case of
(a) the adiabatic compression.
(b) the constant-temperature compression.
(c) In both processes the amount of work is the same.
4. Gas in a piston expands its volume at constant pressure. Choose the correct statement:
(a) The internal energy of the gas increases.
(b) The entropy of the gas increases.
(c) The work done by the gas exceeds the amount of heat injected into it.
(d) The heat injected into the gas exceeds the work done by it.
(e) more than one is correct
5. In the path shown below, the gas returns to its original state. The net work done on the gas along this path is
(a) negative.
(b) zero.
(c) positive.
Practice problems for Exam II
Instructor: Cheryl Davis
No time limit, closed book, equation sheet on the test,Calculatorpermitted
Useful information
,, , , , , , , , ,
1. (a) Using information at the top of this sheet, derive the conversions from Fahrenheit to Kelvin and back: and.
2. (a) A steel bridge is 518m long. How much does its length change between temperature extremes of and ?
(b) An automobile fuel tank is filled to the brim with 50L of gasoline at . Immediately afterward, the vehicle is parked in the Sun where the temperature reaches . How much gasoline overflows from the tank as a result of expansion? Neglect the expansion of the tank.
3. Calculate the number of molecules in 1L of air near the earth's surface (1atm)
(a) on a hot day ().
(b) and on a cold day ().
4. Ice water inside a Styrofoam cooler contains 1.0kg of ice at. In a room at the ice completely melts in 8hrs. How long would the same amount of ice last if the cooler is outdoors where the temperature is ? HINT: You do not need to know the latent heat of melting. Also, is irrelevant since there is no change in temperature.
5. (a) How much work is done by 3.7mol of an ideal gas as it expands to 6.8 times its initial volume at a constant temperature of ?
(b) What is the heat flow into the gas during this process?
6. A vacuum chamber is contaminated with water vapor at .
(a) What is the rms speed for molecules in the container? Note: A water molecule has a mass of .
7. H2 gas is allowed to expand from an initial state of to a final state of along a path that forms a straight line on a PV diagram.
(a) Draw a PV-diagram of the process.
(b) What is the work done by the gas?
(c) What is the change in internal energy of the gas?
(d) What is the heat injected into the gas during this process?
8. A piston holds an ideal gas consisting of monatomic molecules. The initial. volume is 1.0L. 100J of heat is added to the gas. If the pressure is held constant at 1.0105 Pa during this process, what is the final volume?
9. Two separate containers (label them 1 and 2) with the same initial volumes are filled with a diatomic gas such as N2 at temperature . The molecules do not vibrate internally but may rotate (the case near room temperature). Container 1 is in contact with a thermal reservoir at constant temperature . Container 2 is in complete thermal isolation. The volume of each container is allowed to expand gradually to twice the initial volumes.
(a) Depict the two processes on a single PV diagram.
(b) What is the ratio of the final pressure in container 1 to the final pressure in container 2?
10. A Carnot engine does 400J of work and expels 800J of energy into the cold reservoir on each cycle.
(a) What is the efficiency of the engine?
(b) If of entropy is transferred into the cold reservoir on each cycle, what is the temperature of the hot reservoir?
11. A Carnot cycle on a P-V diagram reaches a maximum volume of 5.0L and a minimum volume of 1.0L. Assume that there is 0.1mol of gas and that .
(a) Find the work done per cycle if the temperatures of the two reservoirs are and .
(b) How much entropy is transferred into the gas while in contact with the hot reservoir?
SOLUTION Multiple choice
1. (a) To keep the pressure constant, the piston does work as the volume increases. Since the gas loses internal energy to do work, the temperature does not increase as much.
2. (c) The ideal gas law shows that density of the air to be proportional to the pressure: . Therefore, the velocity of sound in air doesn’t change.
3. (a) Adiabatic compression has a steeper curve on the PV diagram with more area under the curve. Since no heat can escape, the gas heats up during the adiabatic compression causing a higher pressure.
4. (e)
5. (a)
1. (a) (linear connection)
2. (a)
(b)
3. (a)
(b)
4.
5. (a)
(b)
6. (a)
7. (a)
(b) Area below curve: .
(c)
(d)
8. , , , .
Note: We didn’t need to know the initial temperature or number of moles.
9.
10. (a)
(b)
Alternatively:
11. (a)
and (We need )
(b)