AIIMS 2019 Physics Heat Engines MCQ Question

The expression $T_2/T_1 = (V_1/V_2)^{r-1}$ indicates a relationship between temperature and volume for a gas undergoing a process characterized by the specific heat ratio $r$. Substituting $V_1 = 1$ and $V_2 = 3$ into the equation yields $T_2/T_1 = (1/3)^{1.5-1} = (1/3)^{0.5} = 1/\sqrt{3}$, which is approximately 0.577, not 0.5.

Option B (1/2) is incorrect because it does not accurately reflect the calculated ratio. Other options such as 1/3 and 1 are also incorrect as they do not correspond to the derived value of $1/\sqrt{3}$. Understanding the relationship between temperature and volume in thermodynamic processes is crucial for solving such problems.