A sample of an ideal monatomic gas undergoes the two-step transformation described below

PHYSICS · Multi-part · CBSE · Physics · Thermodynamics · Thermodynamics

Problem

A 0.200 mol0.200\,\text{mol} sample of an ideal monatomic gas undergoes the two-step transformation A→B→CA \rightarrow B \rightarrow C described below. • Step 1 (A→BA \rightarrow B): The gas is compressed at constant volume from the initial state A (PA=1.0 atm, V=1.5 L)A\,(P_A = 1.0\,\text{atm},\,V = 1.5\,\text{L}) to the intermediate state B (PB=3.0 atm)B\,(P_B = 3.0\,\text{atm}). • Step 2 (B→CB \rightarrow C): Immediately after reaching state BB, the container is thermally insulated. The gas then expands quasistatically to the final state C (PC=1.0 atm, VC=3.5 L)C\,(P_C = 1.0\,\text{atm},\,V_C = 3.5\,\text{L}). No other interactions with the surroundings occur. (a) Identify the thermodynamic process type for step 1 and for step 2. Explain your reasoning for each step. (b) Calculate the work done ON the gas during step 1. (c) For step 2, determine the work done ON the gas. (You may express your answer in terms of an integral if you do not carry out an explicit numerical evaluation.) (d) Using your results and the first law of thermodynamics, state whether the internal energy of the gas increases, decreases, or remains unchanged over the entire two-step transformation A→CA \rightarrow C. Justify your answer qualitatively.

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