Question

One mole of an ideal monoatomic gas at temperature T0 expands slowly according to the law $\frac{P}{V}$= constant. If the final temperature is 2T0, heat supplied to the gas is

• A. 2RT0
• B. RT0
• C. $\frac{3}{2}$RT0
• D. $\frac{1}{2}$RT0

Answer 1

Answer: (A)

2RT0

Answer 2

In a process $PV^{x} =$constant, molar heat capacity is given by

$C = \frac{R}{\gamma - 1} + \frac{R}{1 - x}$

As the process is $\frac{P}{V}$= constant, i.e., $PV^{- 1} =$constant, therefore, $x = - 1.$

For an ideal monoatomic gas, $\gamma = \frac{5}{3}$

$\therefore C = \frac{R}{\frac{5}{3} - 1} + \frac{R}{1 - ( - 1)} = \frac{3}{2}R + \frac{R}{2} = 2R$

$\Delta Q = nC(\Delta T) = 1(2R)(2T_{0} - T_{0}) = 2RT_{0}.$