PHYSICS 221 Summer 2013

Homework 8 Wednesday August 7, 2013

1. Two moles of an ideal diatomic gas have an initial pressure of 4.00 atm and initial volume of 16.0 L. The molecules in the gas can translate and rotate but not vibrate. The gas is compressed at constant pressure to a new volume of 8.00 L.

(a) What are the initial and final temperatures of the gas?

(b) How much work is done by the gas during this process?

(c) How much heat is absorbed by the gas during this process?

(d) What is the change in the internal energy of the gas during this process?

2. An ideal gas mixture consists of n1 moles of a pure gas whose molar heat capacity at constant volume is R/ (γ1 − 1) and n2 moles of a pure gas whose molar heat capacity at constant volume is R/ (γ2 − 1). Find:

(a) the total heat capacity (at constant volume) of the sample, and

(b) the total heat capacity at constant pressure.

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PHYSICS 221 Summer 2013

Homework 8 Wednesday August 7, 2013

3. 4 moles of an ideal gas have an initial temperature of 127 ◦C. The temperature of the gas is kept constant and the volume is increases until the pressure drops to 40.0% of its original value.

(a) Draw a p−V diagram for this process (b) Calculate the work done by the gas.

(c) What is the change in internal energy of the gas?

(d) Calculate the heat added to the gas.

4. A gas with a volume of 4.0 L is at a pressure of 1.0 atm at a temperature of 300 K. It is compressed adiabatically to a volume of 1.0 L. The gas has γ = 1.4.

(a) Determine the final pressure.

(b) Determine the final temperature.

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PHYSICS 221 Summer 2013

Homework 8 Wednesday August 7, 2013

5. Four moles of an ideal monatomic gas, with a ratio of heat capacities γ = 1.67, initially have a pressure p1 = 2.00 atm, a volume V1 = 45.0 L and a temperature T1. Then the gas undergoes the following three-step cyclic process, as shown in the p−V diagram below.

(i) Adiabatic expansion from the temperature T1, pressure p1, and volume V1 to a temperature T2, volume V2 = 65.0 L and pressure p2.

V (L)

p(Tm)

45 50 55 60 65 70

2 1

2

3 i

ii

iii

(ii) Increase in pressure at constant vol- ume to a pressure p3 and a temper- ature T3.

(iii) Isothermal compression to the orig- inal starting pressure, volume, and temperature.

(a) What is T1?

(b) What are T2 and p2?

(c) What are T3 and p3?

(d) From the figure, is the net work done by the gas during the cycle positive or negative?

(e) What is the work done by the gas during each of the three steps of the cycle? What is the net work done by the gas during the entire cycle?

(f) How much heat is absorbed by the gas during each of the three steps of the cycle? What is the net heat absorbed by the gas during the entire cycle? Why should this last result be exactly the same as the last result in part (e)?

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PHYSICS 221 Summer 2013

Homework 8 Wednesday August 7, 2013

6. A diatomic ideal gas is taken through the cycle shown in the figure in the direction a → b → c → a. What is the efficiency of this cycle?

V (m3)

p(×105 Pa)

0.500 0.800

1.00

3.00 a b

c

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