Question

$105$ calories of heat is required to raise the temperature of $3$ moles of an ideal gas at constant pressure from ${30}^{o}C$ to ${35}^{o}C$. The amount of heat required in calories to raise the temperature of the gas through the range $({60}^{o}C$ to ${65}^{o}C)$ at constant volume is: $(\gamma =\frac{C_p}{C_v}=1.4)$

• A. $50$ cal
• B. $75$ cal
• C. $70$ cal
• D. $90$ cal

Answer 1

The correct option is B $75$ cal

Solution:- (B) $75cal$

Heat required to raise the temperature $\left(Q_P\right)=105cal$

Number of moles of gas $\left(n\right)=3\text{mole}$

Increase in temperature $\left(\Delta T\right)=35-30=5$

Now as we know that,

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

$\Rightarrow 105=3\times C_p\times 5$

$\Rightarrow C_p=7$

Given that:-

$\frac{C_p}{C_v}=1.4$

$\therefore C_v=\frac{C_P}{1.4}=\frac{7}{1.4}=5$

Therefore, the quantity of heat required to increase the temperature by $5℃$ at constant volume is-

$Q_v=n{C}_v\Delta T$

$\Rightarrow Q_v=3\times 5\times 5=75cal$

Hence the heat required is $75cal$.