Question

Two cylinders $A$ and $B$ fitted with pistons contain equal amounts of an ideal diatomic gas at $300 \, K$ . The piston of $A$ is free to move, while that of $B$ is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $30 \, K$ , then the rise in temperature of the gas in $B \, $ is.

• A. $30\,K$
• B. $18\,K$
• C. $50\,K$
• D. $42\,K$

Answer 1

Answer: (D)

A is free to move; therefore, heat will be supplied at constant pressure.
$\Delta Q_{ A }=n C_{ P _{ A }} \Delta T_{ A } \ldots $ (i)
$B$ is held fixed, therefore, heat will be supplied at constant volume.
$\Delta Q_{ B }=n C_{ V }{ }_{ B } \Delta T_{B} .....$ (ii)
But $\Delta Q_{ A }=\Delta Q_{ B }$
$nC _{ P _{ A }} \Delta T_{A}= nC _{ V _{ B }} \Delta T_{B}$
$\Delta T_{ B }=\left(\frac{ C _{ P }}{ C _{ V }}\right) \Delta T_{ A } $
$=\gamma\left(\Delta T_{ A }\right) \left(\gamma=1.4\left(\text { diatomic) }\left(\Delta T_{ A }=30\, K \right)\right.\right. $
$=(1.4)(30\, K ) $
$\Delta T_{ B }=42 \,K$