Question

$70$ calories of heat are required to raise the temperature of $2$ moles of an ideal gas at constant pressure from ${30}^{o}C$ to ${35}^{o}C$. The amount of heat required to raise the temperature of same gas through the same range $\left({30}^{o}Cto{35}^{o}C\right)$ at constant volume $(R=2cal/mol/K)$ is:

• A. $30$
• B. $50$
• C. $70$
• D. $90$

Answer 1

The correct option is B $50$

Given: Heat required to raise the temperature

$Q_P=70cal$

$n=2moles$

$\Delta T=5^{o}C$

$Q_P=n{C}_P\Delta T$

$\Rightarrow 70=2\times C_P\times 5$

$\Rightarrow C_P=7cal/mol/K$

$\therefore C_V=5$ (As for gas $C_P-C_V=R$)

Now, that required to increase the temperature at constant volume,

$Q_V=n{C}_V\Delta T=2\times 5\times 5=50cal$