Question

If heat is added at constant volume, 6300 J of heat are required to raise the temperature of an ideal gas by 150 K. If instead, heat is added at constant pressure, 8800 joules are required for the same temperature change. When the temperature of the gas changes by 300 K. Determine the change is the internal energy of the gas.

Answer 1

Heat added at constant volume is equal to the change in internal energy of the system.

Change in internal energy $\Delta U=n{C}_v\Delta T$

For $\Delta T=150K$, $\Delta U=Q_v=6300$ J

$\therefore$ $6300=n{C}_v\left(150\right)$ .........(1)

Let the change in internal energy be $\Delta U$ for $\Delta T=300K$

$\therefore$ $\Delta U=n{C}_v\left(300\right)$ .........(2)

Dividing (2) and (1) we get $\frac{\Delta U}{6300}=\frac{300}{150}$

$⟹\Delta U=12600$ J