Question

An ideal gas initially at 0°C temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is \( \frac{3}{2} \), the change in temperature due to the thermodynamics process is         K.

Hint:

The change in temperature can be derived using the thermodynamic relation between pressure, volume, and temperature for adiabatic processes. Use the initial and final conditions to calculate the change.

Answer 1

Given that \( \gamma = \frac{3}{2} \), we use the relation: \[ T V^{\gamma - 1} = C \] Substitute the given values: \[ 273 V_0^{0.5} = T \left( \frac{V_0}{4} \right)^{0.5} \] Solving for \( T \): \[ T = 273 \times 2 = 546 \] Thus: \[ \Delta T = 273 \, \text{K} \]