Question

Two identical glass bulbs are interconnected by a thin glass tube. A gas is filled in these bulbs at NTP. If one bulb is placed in ice and another bulb is placed inside a hot bath, then the pressure of the gas becomes $1.5$ times. The temperature of the hot bath will be

• A. $100^\circ C$
• B. $182^\circ C$
• C. $256^\circ C$
• D. $546 \,{}^\circ C$

Answer 1

Answer: (D)

Quantity of gas in these bulbs is constant, i.e.,
initial no. of moles in both the bulbs = final number of moles
$\mu _{1} + \mu _{2} = \mu _{1}^{'} + \mu _{2}^{'}$
$\frac{\textit{PV}}{\textit{R} \left(2 7 3\right)}+\frac{\textit{PV}}{\textit{R} \left(2 7 3\right)}=\frac{\text{1.5} \textit{PV}}{\textit{R} \left(2 7 3\right)}+\frac{\text{1.5} \textit{PV}}{\textit{R} \left(\textit{T}\right)}$
$\Rightarrow \frac{2}{2 7 3}=\frac{1 . 5}{2 7 3}+\frac{\text{1.5}}{T}$
$\Rightarrow T=819K=546^\circ C$