An ideal monatomic gas sample (1.00 mol) is taken through the following three-step cycle

PHYSICS · Multi-part · A Level · Physics · Engineering physics · Engineering physics

Problem

An ideal monatomic gas sample (1.00 mol) is taken through the following three-step cycle. Step 1 Isothermal expansion at

300\,\text{K}

from 1.00 atm to 0.500 atm. Step 2 Cooling at 0.500 atm from

300\,\text{K}

250\,\text{K}

. Step 3 Isothermal compression at

250\,\text{K}

from 0.500 atm back to 1.00 atm. Assume ideal-gas behavior throughout and that

R=8.314\,\text{J mol}^{-1}\,\text{K}^{-1}

. (a) Calculate the entropy change for the gas in Step 1. (b) Calculate the entropy change for the gas in Step 2. (c) Calculate the entropy change for the gas in Step 3. (d) Determine the net entropy change for the gas over the complete three-step cycle and interpret the result in terms of state-function properties. (e) Suppose Step 3 were performed at

275\,\text{K}

instead of

250\,\text{K}

while Steps 1 and 2 remained unchanged. Predict qualitatively (no calculation required) whether the overall entropy change for the gas would be positive, negative, or zero, and justify your reasoning.

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