An ideal gas is taken reversibly from state A (P, V) to the state B (0.5 P, 2 V) along a straight li — Thermodynamics and Thermochemistry Chemistry Question
Question
An ideal gas is taken reversibly from state A (P, V) to the state B (0.5 P, 2 V) along a straight line in PV diagram. Which of the following statement(s) is/are correct regarding the process?
💡 Solution & Explanation
For a straight line path from (P, V) to (0.5P, 2V), the equation of the line is P = 1.5P_0 - 0.5(P_0/V_0)*V. Work done is the area under the straight line (trapezium): 0.5*(P + 0.5P)*(2V - V) = 0.75PV. For isothermal process, W = PV ln(2) = 0.693PV. Since 0.75PV > 0.693PV, work done exceeds isothermal work (A correct). T is ∝ PV = V*(1.5P_0 - 0.5(P_0/V_0)*V), a quadratic function of V (downward parabola), so T increases to a maximum then decreases (D correct). In T-V diagram, T is quadratic in V — a parabola (B correct). In P-T diagram, T is quadratic in P — also a parabola, not hyperbola (C incorrect).