The correct relation between = CpCv and temperature T is: — Solution | JEE Physics

MCQEasyJEE 2023Equation of State of Ideal Gas

The correct relation between $\gamma = \frac{C_p}{C_v}$ and temperature $T$ is:

A
$\gamma \propto \frac{1}{\sqrt{T}}$
B
$\gamma \propto T^0$
C
$\gamma \propto \frac{1}{T}$
D
$\gamma \propto T$

Answer

Correct answer:B

Step-by-step solution

Standard Method

Given: The relation between $\gamma = \frac{C_p}{C_v}$ and temperature $T$ is asked.

Find: Which option correctly describes how $\gamma$ depends on $T$ .

For an ideal gas, the specific heat ratio $\gamma$ is independent of temperature over the usual range considered here. Therefore, $\gamma$ remains constant with change in $T$ .

This is written as:

\gamma \propto T^0

Hence, the correct relation is $\gamma \propto T^0$ .

The solution states option A, but that is inconsistent with the listed options and with the written conclusion. The defensible correct option from the provided options is B.

Common mistakes

Assuming that $\gamma$ varies directly with temperature. This is incorrect for the ideal-gas treatment used here. Instead, identify that $\gamma = \frac{C_p}{C_v}$ is taken as approximately constant.
Reading the option label from the solution without checking the actual expression. The solution text says option A, but the expression written is $\gamma \propto T^0$ , which matches option B in the given list. Always match the formula, not only the label.

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Answer

Step-by-step solution

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