One mole of a non-ideal gas is heated at constant volume from (4 bar, 12 L, 240 K) to (6 bar, 12 L, 360 K), and then at constant pressure to (6 bar, 20 L, 600 K).
Given (assume constant): C_V = 25 J/mol/K, C_P = 33 J/mol/K.
Find ΔU for the overall change.

Question

One mole of a non-ideal gas is heated at constant volume from (4 bar, 12 L, 240 K) to (6 bar, 12 L, 360 K), and then at constant pressure to (6 bar, 20 L, 600 K).

Given (assume constant): C_V = 25 J/mol/K, C_P = 33 J/mol/K.

Find ΔU for the overall change.

TestHub · Accepted Answer

Non-ideal gas, so ΔU ≠ nC V ΔT for the whole path (9000 J is the trap). Step 1 (constant V): w = 0, so ΔU = q = C V ΔT = 25 × 120 = 3000 J. Step 2 (constant P): q = ΔH = C P ΔT = 33 × 240 = 7920 J. Work done by gas in step 2 = 6 × 8 = 48 bar L = 4800 J. ΔU 2 = 7920 - 4800 = 3120 J. Total ΔU = 3000 + 3120 = 6120 J. Answer: (C).

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