Question

An ideal gas undergoes a thermodynamic process following the relation PT² = constant. Assuming symbols have their usual meaning then volume expansion coefficient of the gas is equal to

• A. \(\frac{2}{T}\)
• B. \(\frac{3}{T}\)
• C. \(\frac{1}{2T}\)
• D. \(\frac{1}{T}\)

Answer 1

The Correct Option is B

Given: 

\[ \frac{dV}{V} = \alpha \frac{dT}{T} \]

For a constant \( P T^2 \), we have:

\[ \frac{dV}{dT} = \left( C \right) \frac{3}{T^2} \]

So, the volume expansion coefficient is:

\[ \frac{dV}{V} = \frac{3}{T^2} \cdot dT \]