Q 11-11-053JEE MainJEE Main 2025 (24 Jan, Shift 1)Easy
The temperature of 1 mole of an ideal monoatomic gas is increased by $50^\circ\text{C}$ at constant pressure. The total heat added and change in internal energy are $E_1$ and $E_2$, respectively. If $\dfrac{E_1}{E_2} = \dfrac{x}{9}$, then the value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 15
At constant pressure $E_1 = nC_p\Delta T$ and $E_2 = nC_v\Delta T$, so
$$\frac{E_1}{E_2} = \frac{C_p}{C_v} = \gamma = \frac{5}{3} = \frac{15}{9}$$
$x = 15$
Solution by Sreeraj P, M.Sc Physics