Practice Exam

9/16/98

1. a) Derive the equation for the heat of a reversible, isothermal expansion of one mole of an ideal gas from P1 to P2.

b) Calculate q, w, DU involved in the reversible isothermal expansion of 2 moles of He from 1.4 bar to 0.65 bar at 45 oC. (Assume an ideal gas).

 

2. Derive either the equation

Cvln(T2/T1) = -R ln(V2/V1) for a reversible adiabatic expansion of one mole of an ideal gas.

or the equation Cpln(T2/T1) = R ln(P2/P1) for a reversible adiabatic expansion of one mole of an ideal gas.

 

3. Give just the signs of the following functions for the following processes as 0 or + or -.

Process q w DT DU DV DH DP
Reversible Isothermal Expansion of and ideal Gas         +    
Reversible Adiabatic Expansion of an ideal gas         +    
Reversibly heating a gas at constant pressure.              
Irreversible expansion of an ideal gas into a vacuum.              

4. What is the change in temperature of a diatomic gas if it is expanded adiabatically and irreversibly against a constant pressure of 1 bar if its initial temperature is 23 C and its internal pressure is 1.2 bar and its final pressure is 1 bar.

5. 130 g of a metal at 87 oC are added to a calorimeter system that has a initial heat capacity of 387 J/oC and is a temperature of 24.7 oC. The temperature of the calorimeter increases to 28.2 C. What is the heat capacity of the metal?

6. Derive the relation Cp = Cv+R.

7. A mole of an ideal monatomic gas is heated at a constant pressure of 2 bar from 35 oC to 85 oC and then undergoes a reversible isothermal expansion to double its volume. This is followed by a reversible adiabatic compression to the original pressure. The gas is then cooled at constant volume to 25 oC. What is the change in energy of the gas?