Textbook Question
Heat Q flows into a monatomic ideal gas, and the volume increases while the pressure is kept constant. What fraction of the heat energy is used to do the expansion work of the gas?
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Ch 19: The First Law of Thermodynamics
Chapter 19, Problem 19
Figure E19.8 shows a pV-diagram for an ideal gas in which its absolute temperature at b is one-fourth of its absolute temperature at a. 
(d) Did heat enter or leave the gas from a to b? How do you know? 
Verified step by step guidance1
Identify the type of process: The pV-diagram shows a horizontal line from point a to point b, indicating an isobaric process (constant pressure).
Use the ideal gas law: For an isobaric process, the relationship between temperature and volume is given by \( \frac{T_a}{T_b} = \frac{V_a}{V_b} \).
Given that the temperature at b is one-fourth of the temperature at a, we have \( T_b = \frac{1}{4} T_a \).
Substitute the given temperatures into the ideal gas law relationship: \( \frac{T_a}{\frac{1}{4} T_a} = \frac{V_a}{V_b} \).
Simplify the equation to find the relationship between the volumes: \( 4 = \frac{V_a}{V_b} \), which implies \( V_b = \frac{1}{4} V_a \). Since the volume decreases from a to b, the gas is compressed, indicating that heat has left the gas.
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