Question

$4.48L$ of an ideal gas at S.T.P requires $12$ calories to raise its temperature by ${15}^{o}C$ at constant volume. The $C_p$ of the gas is:

• A. $3cal$
• B. $4cal$
• C. $7cal$
• D. $6cal$

Answer 1

The correct option is D $6cal$

At STP, 22.4L of ideal gas = 1 mole

Heat required $=n{C}_V\Delta T$

$\therefore 12=\frac{4.48}{22.4}\times C_V\times 15$

$\therefore C_V=0.4cal/mol.K$

Now, $C_P-C_V=R$

$\therefore C_P=C_V+R$

$\therefore C_P=0.4+5.6$ (R=5.6 cal/mol.K)

$\therefore C_P=6Cal$

Hence, the correct option is $D$