Two moles of helium are initially at a temperature of 27.0°C and occupy a volume of 0.0300 m? . The helium first expands at constant pressure until its volume has doubled. Then it expands adiabatically until the temperature returns to its initial value. Assume that the helium can be treated as an ideal gas (a) Draw a diagram of the process in the ?pV – plane. (b)What is the total heat supplied to the helium in the process? (c) What is the total change in internal energy of the helium? (d) What is the total work done by the helium? (e) What is the final volume of the helium?

Solution 50P Step 1: Ideal gas equation, PV = nRT Where, P - Pressure of the gas V - volume of the gas n - Number of moles of the gas R - Universal gas constant T - temperature of the gas Step 2: Provided, n = 2 moles Therefore, initially, PV = 2RT 1 After that, it expands at constant pressure until the volume is getting doubled. That is, 2PV = 2RT 2 Therefore, We can say that, 2×2 RT = 2RT 1 2 Or, 2RT = RT 1 2 Or, T2 2T 1 Step 3: a) Step 4: b) Total heat supplied to the helium, Q = nC T V Provided, n = 2 moles, C for diVomic molecule = 5/2 R T = T - 2 = 1 - T1 T1 1 Provided, T = 1 = 27 + 273 = 300 K Therefore, Q = 2 × 5/2 R × 300 K Q = 2 × 5/2 × 8.314 J/mol K × 300 K = 12471 J