Q 11-12-129JEE MainJEE Main 2020 (3 Sep, Shift 2)Medium
To raise the temperature of a certain mass of gas by $50^\circ\text{C}$ at a constant pressure, $160$ calories of heat is required. When the same mass of gas is cooled by $100^\circ\text{C}$ at constant volume, $240$ calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?
Answer: (B) $6$
$nC_P\times50 = 160 \Rightarrow nC_P = 3.2$; $nC_V\times100 = 240 \Rightarrow nC_V = 2.4$.
$$\gamma = \frac{C_P}{C_V} = \frac43 = 1 + \frac2f \Rightarrow f = 6$$
Solution by Sreeraj P, M.Sc Physics