Question

Two cylinders contain same amount of ideal monatomic gas. Same amount of heat is given to two cylinders. if temperature rise in cylinder A is $T_o$ then temperature rise in cylinder B will be

• A. $\frac{4}{3}{T}_o$
• B. $2T_o$
• C. $\frac{T_o}{2}$
• D. $\frac{5}{3}{T}_o$

Answer 1

The correct option is D $\frac{5}{3}{T}_o$

For both cylinders, heat supplied:
$\Delta Q_1=\Delta Q_2......\left(i\right)$
For cylinder with free piston, gas will expand to maintain a constant pressure always.
$\Rightarrow P$ = constant
$\Rightarrow \Delta Q_1=n{C}_p\Delta T$
$\Rightarrow \Delta Q_1=n{C}_p{T}_o......\left(ii\right)$
For cylinder with Fixed piston (constant volume process),
$V=$ constant
$\Rightarrow \Delta Q_2=n{C}_v\Delta T.....\left(iii\right)$
From Eq. (i)
$\Rightarrow n{C}_p{T}_o=n{C}_v\Delta T$
$\Rightarrow \Delta T=\left(\frac{C_p}{C_v}\right)T_o=\gamma T_o$
Monoatomic gas $(\gamma =5/3)$
$\therefore \Delta T=\frac{5}{3}{T}_o$