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.