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Chapter 18: Problem 13

Why is specific heat at constant pressure greater than at constant volume?

Short Answer

Expert verified
Specific heat at constant pressure (Cp) is greater than at constant volume (Cv) because at constant pressure, the substance does work along with the increase in its internal energy (or temperature), using the heat supplied, whereas at constant volume, all the heat supplied only increases its internal energy. Mathematically, it is due to the equation Cp - Cv = R, where R is positive hence making Cp greater than Cv.

Step by step solution

01

Understanding Constant Pressure and Volume

In thermodynamics, there are two types of specific heat defined: constant volume (Cv) and constant pressure (Cp). Cv is the amount of heat required to raise the temperature of a substance by one degree, while keeping volume constant. Conversely, Cp is done while keeping pressure constant.
02

Understand the Difference between Cp and Cv

When heat is added at constant pressure, the substance does some work along with the increase in temperature, because the volume can change. However, at constant volume situation, all the added heat only contributes to increase in temperature as the substance cannot do work as Now there is no volume change. Therefore, Cp is usually greater than Cv.
03

Unveiling the Mathematical Reason

Mathematically, this can be seen from the equation: Cp - Cv = R, where R is the gas constant. Since R is always positive, Cp is always greater than Cv.

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