For a gas, the molar specific heat at constant pressure Cp is greater than that at constant volume Cv because
Correct answer: B. at constant pressure the gas also does work expanding against the surroundings
- A. the gas is hotter at constant pressure
- B. at constant pressure the gas also does work expanding against the surroundings
- C. the molecules move faster at constant pressure
- D. Cv is measured at a lower temperature
Explanation
At constant volume all the heat supplied raises the internal energy, but at constant pressure some of it is spent doing work as the gas expands, so more heat is needed for the same temperature rise. The difference is exactly the gas constant R, which is Mayer's relation. This is why Cp always exceeds Cv for any gas.
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About Molar Specific Heat of a Gas
Molar specific heat is the heat required to raise the temperature of one mole of a gas by one kelvin, expressed through Q = nCΔT. Questions compare the constant volume value Cv with the constant pressure value Cp, apply the ideal gas relation Cp − Cv = R, and identify how the thermodynamic process affects heat capacity.
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