Question

The temperature of a sample of dilute argon gas with n = 6.8 moles decreases by 196 K during a thermodynamic process. If 35,000 J of heat are extracted from the gas, what is the work done by the gas on its surroundings? _____J

Answer 1

By changing the temperature ?T its internal energy changes by
?U = n?Cv??T

n is the number of moles and Cv is the molar heat capacity at constant volume. Don't get confused about the wording. Relation above holds for every process, even if the volume change.
For argon:
Cv = 12.4717J/molK

Hence:
?U = 7.8mol ? 12.4717J/molK ? (-196K) = -19066.734J

On the other hand change of internal energy equals heat transferred to the gas plus work done on the gas:
?U = Q + W

Therefore:
W = ?U - Q
= -19066.734J - (-35000J)
= 15933.266J