What is the relationship between heat capacity at constant volume (Cv) and heat capacity at constant pressure (Cp) for an ideal gas?

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Q: What is the relationship between heat capacity at constant volume (Cv) and heat capacity at constant pressure (Cp) for an ideal gas?

Solution: For an ideal gas, the relationship is given by Cp = Cv + R, where R is the universal gas constant.

Steps: 6

Step 1: Understand what heat capacity means. Heat capacity is the amount of heat needed to change the temperature of a substance.
Step 2: Know that there are two types of heat capacity: at constant volume (Cv) and at constant pressure (Cp).
Step 3: Recognize that for an ideal gas, the heat capacity at constant pressure (Cp) is always greater than the heat capacity at constant volume (Cv).
Step 4: Learn the formula that relates Cp and Cv for an ideal gas: Cp = Cv + R.
Step 5: Identify R as the universal gas constant, which is a specific value (approximately 8.314 J/(mol·K)).
Step 6: Conclude that the difference between Cp and Cv is equal to the universal gas constant (R).