Question

Two cylinders A and B fitted with pistons contain an equal number of moles of an ideal monoatomic gas at $400K$. The piston of A is free to move while that of B is held fixed. The same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in A is $42K$, the rise in temperature of the gas in B is

• A. $21K$
• B. $35K$
• C. $42K$
• D. $70K$

Answer 1

The correct option is C $42K$

From first law of thermodynamics
$Q=\Delta U+W$
For cylinder A pressure remains constant
$\therefore$ Work done by a system
$W=\frac{\mu R}{\gamma -1}{T}_1-T_2$
For monatomic gases
$\mu =1$
$\gamma =\frac{5}{3}$
$\therefore W=\frac{1\times R}{5}442-400=\frac{3}{2}R\times 42$
or $W=63R$
But $\Delta =0,$ for cylider A
$Q=0+63R$
$Q=63R$
For cylinder B Volume is constant,
$\therefore W=0$
and $Q=\mu C_v\Delta T$
For mono atomic gas
$C_V=\frac{3}{2}R$
$Q=1\times \frac{3}{2}R\Delta T$
As heat given to both cylinder is game
$\therefore 63R=\frac{3}{2}R\Delta T$
$\Delta =42K$