Problem 2.3.4

 

An ideal gas is compressed isothermally from 1 atmosphere and 294.3 degrees Kelvin to a final pressure of 5 atmospheres.  Heat capacity at constant pressure is given as 7 calories per mole per degree Kelvin.  Heat capacity at constant volume is given as 5 calories per mole per degree Kelvin.  Gas law constant is 8.32 Pa. cubic meter per mole per degree Kelvin.  What is change in the internal energy, enthalpy and entropy?  How much work is done and how much heat is added or removed.  What are values of temperature and volume at the end of the operations?    

 

Solution: 

 

For an isothermal process, final temperature is the same as 294.3 degrees Kelvin.

 

Internal energy change, delta U, is equal to integral from T1 to T2 of CV dT.  Delta U is zero. 

 

Enthalpy change, delta H is equal to integral from T1 to T2 of CP dT.  For a constant value of CP, this simplifies to CP time (T2 minus T1).  Delta H is calculated as 3,228 joules per mole.

 

Work done by the system, W, is minus RT1 log (P2 over P1).  This value is calculated as -3,895 joules per mole.  Minus sign indicates work is done on the system.

 

Heat added to the system is delta U plus W or -3,895 joules per mole.

 

Entropy change is equal to R log of P1 over P2.  Entropy change is calculated to be minus 13.2 joules per mole per degree Kelvin.

 

Initial volume, V1, of the gas can be found by RT1 over P1.  V1 is calculated to be 0.0237 cubic meters per mole.  Note that 1 atmosphere is equal to 1.01325 times 105 Pascals. 

 

Final volume, V2, of the gas can be found by V1 time (P1 over P2).  This is calculated to be 4.83 times 10-3 cubic meters per mole.