Question

A mass of an ideal gas of volume V at pressure P undergoes the cycle of changes shown in the graph

At which points is the gas coolest and hottest?

	coolest	hottest
(a)	X	Y
(b)	Y	X
(c)	Y	Z
(d)	Z	Y

• A. a
• B. b
• C. c
• D. d

Answer 1

Answer: (D)

$\frac{P_X{V}_X}{T_X}=\frac{P_Y{V}_Y}{T_Y}=\frac{P_Z{V}_Z}{T_Z}$
$\Rightarrow \frac{(4)(1)}{T_X}=\frac{(1)(5)}{T_Y}=\frac{(1)(1)}{T_Z}$
$\Rightarrow \frac{T_X}{4}=\frac{T_Y}{5}=\frac{T_Z}{1}$
$\Rightarrow T_Z$ is coolest and $T_Y$ is hottest.