Molar specific heats Cp and Cv (Mayer's relation)
Laws of thermodynamics · Physics
Gas piston lab
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Study notes
Step 1: Given data – 1 mole of an ideal gas, Cv = 20 J/(mol·K).\nStep 2: Find Cp using Mayer’s relation: Cp = Cv + R = 20 + 8.314 = 28.314 J/(mol·K).\nStep 3: Add 200 J of heat at constant volume. Temperature change ΔT = Q/Cv = 200 / 20 = 10 K. New temperature = 300 K + 10 K = 310 K.\nStep 4: Find heat required at constant pressure to raise the same 1 mole by 10 K: Qp = Cp × ΔT = 28.314 × 10 = 283.14 J.\nResult: At constant volume, 200 J raises temperature by 10 K. At constant pressure, 283.14 J is needed for the same temperature rise.