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

The correct answer is (B) : \(\frac{3}{T}\)
Volume expansion coefficient = \(\frac{dV}{VdT}\)
For PT² = constant
Or \(\frac{T^3}{V}\) = constant
Or \(\frac{dV}{dT}=(C)3T^2\)
Or \(\frac{dV}{VdT}=\frac{3T^2}{T^3}\)
\(\frac{dV}{VdT}=\frac{3}{T}\)