A fixed mass of an ideal gas undergoes two distinct adiabatic expansion processes. Process A takes the gas from an initial state (P₁, V₁) to a final state (P₂, V₂) . Process B takes the same gas from a different initial state (P₃, V₃) to a

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A fixed mass of an ideal gas undergoes two distinct adiabatic expansion processes. Process A takes the gas from an initial state (P₁, V₁) to a final state (P₂, V₂) . Process B takes the same gas from a different initial state (P₃, V₃) to a final state (P₄, V₄) . It is observed that both processes start at the same initial temperature T₁ and end at the same final temperature T₂ . If W_A and W_B represent the magnitude

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Correct answer: C. W_A = W_B

For an adiabatic process, the heat exchange is zero ( Q = 0 ). According to the first law of thermodynamics, Q = U + W , which gives W = - U . The change in internal energy for an ideal gas is given by U = nC_v T . Since both processes involve the same fixed mass of the same ideal gas (same n and C_v ) and operate between the identical initial and final temperatures (same T ), the change in internal energy is exactly the same for both processes. Therefore, the magnitudes of the work done must be equal, yielding W_A

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