Question

An ideal gas at \(27^{\circ}\)C is compressed adiabatically to \((\frac{8}{27})\) of its original volume. If \(γ = 5/3\), then the rise in temperature of a gas is

• A. \(300\) K
• B. \(675\) K
• C. \(375\) K
• D. \(27\) K

Hint:

Use T V^(gamma - 1) = constant.

Answer 1

The Correct Option is C

Step 1: Use pressure-free form:
Because $\left(\tfrac{27}{8}\right)^{1/3} = \tfrac32$, we get $\left(\tfrac{27}{8}\right)^{2/3} = \tfrac94$.

Step 2: Temperatures:
$T_2 = \tfrac94\times300 = 675$ K.

Step 3: Rise:
$\Delta T = 675 - 300 = 375$ K, option (C).

Final Answer:
The temperature rises by 375 K. \[ \boxed{\text{(C) }375\ \text{K}} \]