Question

70 calories of heat is required to raise the temperature of 2 kg of an ideal gas at constant pressure from ${30}^{o}Cto{35}^{o}C$. The amount of heat required to raise the temperature of the same gas through the same range at constant volume is (Take $\gamma =1.4$).

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

Answer 1

The correct option is B 50 calories

$Q=m{c}_p\Delta T\text{(For constant pressure)}$

$Q^{\prime }=m{c}_v\Delta T\text{(For constant volume)}$

$\therefore$ $70=2\times c_p\times 5....\left(1\right)$

$Q^{\prime }=2\times c_v\times 5.....\left(2\right)$

Using (1) and (2)

$Q^{\prime }=\frac{70}{\left(c_p/v_v\right)}=\frac{70}{\gamma }=\frac{70}{1.4}=50\text{calories}$