2 moles of an ideal monoatomic gas is carried from a state (p₀, V₀ ) to state (2 p₀, 2 V₀ ) along a straight line path in a p-V diagram. The amount of heat absorbed by the gas in the process is given by

Step-by-step solution

The internal energy U=n C_ r TC_ v = Specific heat of gas at constant volume aligned U &=n 3 R 2 ( 4 p₀ V₀ n R - p₀ V₀ n R ) &=n 3 R 2 ( 4 p₀ V₀-p₀ V₀ n R ) &=n 3 R 2 3 p₀ V₀ n R &= 9 2 p₀ V₀ aligned Work done by the gas W= (2 p₀+p₀ ) V₀ 2 = 3 p₀ V₀ 2 From first law of thermodynamics, aligned Q &=d W+d U &= 3 p₀ V₀ 2 + 9 2 p₀ V₀ aligned [from Eqs. (i) and (ii)] array l = 3 p₀ V₀ 2 + 9 2 p₀ V₀ = 12 p₀ V₀ 2 =6 p₀ V₀ array