What is the relationship between heat capacity at constant pressure (C_p) and heat capacity at constant volume (C_v)?

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Q: What is the relationship between heat capacity at constant pressure (C_p) and heat capacity at constant volume (C_v)?

Solution: For an ideal gas, C_p is always greater than C_v due to the work done during expansion.

Steps: 5

Step 1: Understand what heat capacity means. It is the amount of heat needed to change the temperature of a substance.
Step 2: Learn about constant pressure (C_p) and constant volume (C_v). C_p is the heat capacity when pressure is kept the same, while C_v is when volume is kept the same.
Step 3: Recognize that for an ideal gas, when heat is added at constant pressure, the gas can expand and do work on its surroundings.
Step 4: Understand that this work done during expansion requires additional heat, which is why C_p is greater than C_v.
Step 5: Remember the relationship: C_p = C_v + R for an ideal gas, where R is the gas constant.