10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from P₁ to P₂ is α Joule (P₁ = 21.7 Pa and P₂ = 30 Pa, Cv = 21 J/K·mol, R = 8.3 J/mol·K). The value of α i $s ____.$

Question

G1 Physics · Accepted Answer

From the graph, the process from P₁ to P₂ occurs at constant volume V = 1 m³. Therefore the process is isochoric and W = 0. Hence, Q = ΔU = nCᵥΔT. Using the ideal-gas equation, PV = nRT. At constant volume, nRΔT = (P₂-P₁)V. Therefore, Q = (Cᵥ/R)(P₂-P₁)V. Substitute: Cᵥ = 21 J·mol⁻¹·K⁻¹, R = 8.3 J·mol⁻¹·K⁻¹, P₂-P₁ = 30-21.7 = 8.3 Pa, V = 1 m³. Thus, Q = (21/8.3)(8.3)(1) = 21 J. Therefore, α = 21. Correct option: C.

10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from P₁ to P₂ is α Joule (P₁ = 21.7 Pa and P₂ = 30 Pa, Cv = 21 J/K·mol, R = 8.3 J/mol·K). The value of α i s ____.