JEE Advanced 2023 Paper 1 Q06 Physics Thermal Physics Kinetic Theory of Gases Medium

JEE Advanced 2023 Paper 1 · Q06 · Kinetic Theory of Gases

One mole of an ideal gas expands adiabatically from an initial state $(T_A, V_0)$ to final state $(T_f, 5V_0)$. Another mole of the same gas expands isothermally from a different initial state $(T_B, V_0)$ to the same final state $(T_f, 5V_0)$. The ratio of the specific heats at constant pressure and constant volume of this ideal gas is $\gamma$. What is the ratio $T_A/T_B$?

  1. A. $5^{\gamma-1}$
  2. B. $5^{1-\gamma}$
  3. C. $5^\gamma$
  4. D. $5^{1+\gamma}$
Reveal answer + step-by-step solution

Correct answer:A

Solution

Adiabatic: $T_A V_0^{\gamma-1} = T_f (5V_0)^{\gamma-1} \Rightarrow T_A = T_f \cdot 5^{\gamma-1}$. Isothermal: $T_B = T_f$. So $T_A/T_B = 5^{\gamma-1}$.

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