One mole of an ideal monatomic gas undergoes a process described by the equation P = P0 + alpha/V, where P0 and alpha are positive constants. If the volume changes from V0 to 2V0, the change in internal energy of the gas is:

A. 32 P_0 V_0 — The internal energy of an ideal gas depends only on temperature, which is determined by the product of pressure and volume.

JEE Main · PhysicsMedium

$One mole of an ideal monatomic gas undergoes a process described by the equation P = P_{0} + \frac{α}{V}, where P_{0} and α are positive constants. If the volume changes from V_{0} to 2 V_{0}, the change in internal energy of the gas is:$

Show correct answer & step-by-step solution

Correct answer: A — $\frac{3}{2} P_{0} V_{0}$

$The internal energy of a monatomic ideal gas is U = \frac{3}{2} n R T = \frac{3}{2} P V .$
$Using the process equation P = P_{0} + \frac{α}{V}, we find P V = P_{0} V + α .$
$The change in internal energy is Δ U = \frac{3}{2} (P_{2} V_{2} - P_{1} V_{1}) = \frac{3}{2} ((P_{0} (2 V_{0}) + α) - (P_{0} V_{0} + α)) .$
$Simplifying the expression gives Δ U = \frac{3}{2} P_{0} V_{0} .$
$Hence the answer is (A).$