Question

To raise the temperature of a certain mass of gas by $50{}^{\circ }\text{C}$ at a constant pressure, $160\text{calories}$ of heat is required. When the same mass of gas is cooled by $100{}^{\circ }\text{C}$ at constant volume, $240\text{calories}$ of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

• A. $5$
• B. $6$
• C. $3$
• D. $7$

Answer 1

The correct option is B $6$

At constant pressure, heat required

$\Delta Q_1=n{C}_P\Delta T$

$\Rightarrow 160=n{C}_{P}50--\left(1\right)$

At constant volume, heat required

$\Delta Q_2=n{C}_V\Delta T$

$\Rightarrow 240=n{C}_{V}100--\left(2\right)$

Dividing $\left(1\right)$ by $\left(2\right)$, we get

$\frac{160}{240}=\frac{C_P}{C_V}.\frac{50}{100}\Rightarrow \frac{C_P}{C_V}=\frac{4}{3}$

$\gamma =\frac{C_P}{C_V}=\frac{4}{3}=1+\frac{2}{f}$

$(\text{Here},f=\text{degree of freedom})$

$\Rightarrow f=6.$

Hence, option $\left(B\right)$ is correct.