**PHYS 340**

** **

**Homework assignment #3 **due on
February 17

**A. Reading assignment:** text, Chapter 2

**B. Problems from the textbook**: 2.22; 2.25; 2.26; 2.29; 2.30

**C. Additional problems**:

1. One mole of an ideal gas undergoes an isothermal expansion. Find the heat added to the gas in terms of the initial and final volumes and the temperature.

*Answer*: *RT* ln (*V _{f}/V_{i}*)

2. Let 20.9 J of heat be added to a particular ideal gas. As a result, its
volume changes from 50.0 cm^{3} to 100 cm^{3} while the pressure
remains constant at 1.00 atm. (a) By how much did the internal energy of the gas
change? If the quantity of gas present is 2.00 x 10^{-3} mol, find the
molar specific heat at (b) constant pressure and (c) constant volume.

*Answer*: a. 15.9 J; b. 34.4 J/mol.K; c. 26.1 J/mol. K

3. A quantity of ideal monatomic gas consists of *n *moles initially at
temperature *T _{1}. *The pressure and volume are then slowly
doubled in such a manner as to trace out a straight line on a

4. A container holds a mixture of three no reacting gases: *n _{1} *
moles of the first gas with molar specific heat at constant volume

*Answer*: ( *n _{1}C_{1} + n_{2}C_{2} + n_{3}C_{3}*)/(

5. One mole of an ideal diatomic gas undergoes a transition from *a *(5
kPa; 2 m^{3})* *to *c* (2 kPa; 4 m^{3}) along the
diagonal path. The temperature of the gas at point *a *is 1200 K. During
the transition, (a) what is the change in internal energy of the gas, and (b)
how much heat is added to the gas? (c) How much heat must be added to the gas if
it goes from *a *to *c* along the indirect path *abc *with* b*(5
kPa; 4 m^{3})*?*

*Answer: *a. -5 kJ; b. 2.0 kJ; c. 5.0 kJ

6. One mole of oxygen (O_{2}) is heated at constant pressure starting at
0°C. How much heat must be added to the gas to double its volume? (The molecules
rotate but do not oscillate.)

7. Suppose 12.0 g of oxygen (O_{2}) is heated at constant atmospheric
pressure from 25.0°C to 125°C. (a) How many moles of oxygen are present? (The
molar mass for O_{2} is 32 g/mol) (b) How much heat is transferred to
the oxygen? (The molecules rotate but do not oscillate.) (c) What fraction of
the heat is used to raise the internal energy of the oxygen?

*Answer*: a. 0.375 mol; b. 1090 J; c. 0.714

8. Suppose 4.00 mol of an ideal diatomic gas, with molecular rotation but not oscillation, experiences a temperature increase of 60.0 K under constant-pressure conditions. (a) How much heat was added to the gas? (b) How much did the internal energy of the gas increase? (c) How much work was done by the gas? (d) How much did the translational kinetic energy of the gas increase?

9. A mass of gas occupies a volume of 4.3 L at a pressure of 1.2 atm and a temperature of 310 K. It is compressed adiabatically to a volume of 0.76 L. Determine (a) the final pressure and (b) the final temperature, assuming the gas to be an ideal gas for which g = 1.4.

*Answer*: a. 14 atm; b. 620 K

10*. *(a) One liter of gas with g
= 1.3 is at 273 K and 1.0 atm pressure. It is suddenly compressed
(adiabatically) to half its original volume. Find its final pressure and
temperature. (b) The gas is now cooled back to 273 K at constant pressure. What
is its final volume?

11. Let *n *moles of an ideal gas expand adiabatically from an initial
temperature *T _{1} *to a final temperature

12. An ideal gas experiences an adiabatic compression from *P *= 1.0 atm,
*V *= 1.0 x 10^{6} L, *T *= 0.0°C to *P *= 1.0 x 10^{5}
atm, *V *= 1.0 x 10^{3} L. (a) Is the gas monatomic, diatomic, or
polyatomic? (b) What is its final temperature? (c) How many moles of gas are
present? (d) What is the total translational kinetic energy per mole before and
after the compression? (e) What is the ratio of the squares of the rms speeds
before and after the compression?

*Answer*: a. monatomic; b. 2.7 x10^{4} K; c. 4.5 x 10^{4}
mol; d. 3.4 kJ; e. 0.01

13. A sample of ideal gas expands from an initial pressure and volume of 32 atm and 1.0 L to a final volume of 4.0 L. The initial temperature of the gas is 300 K. What are the final pressure and temperature of the gas and how much work is done by the gas during the expansion, if the expansion is (a) isothermal, (b) adiabatic and the gas is monatomic, and (c) adiabatic and the gas is diatomic?

14. An ideal gas, at initial temperature *T _{1} *and initial volume
2 m

*Answer*: 5 m^{3}

15. One mole of an ideal monatomic gas traverses the cycle shown in figure.
Process 1 → 2 takes place at constant volume, process 2 → 3 is adiabatic, and
process 3 → 1 takes place at constant pressure. (a) Compute the heat *Q, *
the change in internal energy *DU *
and the work done *W, *for each of the three processes and for the cycle
as a whole. (b) If the initial pressure at point 1 is 1.00 atm, find the
pressure and the volume at points 2 and 3. Use 1.00 atm = 1.013 x 10^{5}
Pa and *R *= 8.314 J/mol.K.

*Answer*:
a. in joules, in order *Q. **
DU,
W*: 1→2:
3740, 3740, 0; 2→3: 0, -1810, -1810; 3→1: 3220, -1930, 1290; cycle: 520, 0,
-520; b. *V _{2}* = 0.0246 m