Question

The correct relation between $\gamma=\frac{ c _{ p }}{ c _{ v }}$ and temperature $T$ is :

• A. $\gamma \alpha T ^{\circ}$
• B. $\gamma \alpha \frac{1}{T}$
• C. $\gamma \alpha T$
• D. $\gamma \alpha \frac{1}{\sqrt{T}}$

Hint:

For an ideal gas, the ratio of specific heats \( \gamma \) does not change with temperature.

Answer 1

The Correct Option is A

γ is independent of temperature.
The specific heat ratio (γ) is the ratio of specific heat at constant pressure (Cp​) to the specific heat at constant volume (Cv​). In many cases, for ideal gases, the specific heat ratios (γ) are relatively constant over a range of temperatures. For most gases, the specific heat ratio is not directly proportional to temperature, so options (B), (C), and (D) are not accurate representations of the relationship. The most common behavior is for γ to remain approximately constant with changes in temperature, which corresponds to option (A).
So, the correct Option is (A): γ α T^∘