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The heat capacity at constant pressure (Cp) is greater than Cv because when heat is added at constant pressure, the gas is allowed to expand and some of the heat is used as work. At constant volume, the gas cannot expand so no work is done and all the heat goes into raising the temperature of the system.
Like said before, when there is a constant volume, energy cannot be released through work. Therefore, the heat capacity at constant pressure is higher because this added energy through heat can be given off through work and expansion.
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