Figure E$19.8$ shows a $pV$-diagram for an ideal gas in which its absolute temperature at $b$ is one-fourth of its absolute temperature at $a$. Did heat enter or leave the gas from $a$ to $b$? How do you know?

Five moles of an ideal monatomic gas with an initial temperature of $127$°C expand and, in the process, absorb $1500$ J of heat and do $2100$ J of work. What is the final temperature of the gas?

A gas undergoes two processes. In the first, the volume remains constant at $0.200$ m³ and the pressure increases from $2.00\times {10}^5$ Pa to $5.00\times {10}^5$ Pa. The second process is a compression to a volume of $0.120$ m³ at a constant pressure of $5.00\times {10}^5$ Pa. Find the total work done by the gas during both processes.

A gas in a cylinder expands from a volume of $0.110$ m³ to $0.320$ m³ . Heat flows into the gas just rapidly enough to keep the pressure constant at $1.65\times {10}^5$ Pa during the expansion. The total heat added is $1.15\times {10}^5$ J. Find the work done by the gas.

The process $abc$ shown in the $pV$-diagram in Fig. E$19.11$ involves $0.0175$ mol of an ideal gas. What was the lowest temperature the gas reached in this process? Where did it occur?

In Fig. $19.7$a, consider the closed loop $1\to 3\to 2\to 4\to 1$. This is a cyclic process in which the initial and final states are the same. Find the total work done by the system in this cyclic process, and show that it is equal to the area enclosed by the loop.

A gas undergoes two processes. In the first, the volume remains constant at $0.200$ m³ and the pressure increases from $2.00\(\times\)10^5$ Pa to $5.00\(\times\)10^5$ Pa. The second process is a compression to a volume of $0.120$ m³ at a constant pressure of $5.00\(\times\)10^5$ Pa. In a $pV$-diagram, show both processes.