Question

A 1.5-mole sample of an ideal gas is gently cooled at constant temperature 320 K. It contracts from initial volume 19 L to final volume V2. A total of 1.2 kJ of heat is removed from the gas during the contraction process. What is V2? Let the ideal-gas constant R = 8.314 J/(mol • K). 14 L 10 L 12 L 16 L

Answer 1

In an isothermal process for an ideal gas, the change in internal energy is zero, hence by the first law of thermodynamics,

, ie the the change in heat energy is the negative of the work done on the gas.

Using the convention that work done on the gas is positive,

, hence

------------------(1)

Using ideal gas equation in (1)

-----------------------(2)(Using )

Let us integrate the above to get the total heat removed during the entirety of the process

---------------------------------(3)

We are given (Change in heat is negative since heat is taken away from the sytem)

Let us rearrange (3) :

Substituting all the given values,