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
${\mu }_1+{\mu }_2={\mu }_1^{{}^{\prime }}+{\mu }_2^{{}^{\prime }}$
$\frac{\text{PV}}{\text{R}\left(273\right)}+\frac{\text{PV}}{\text{R}\left(273\right)}=\frac{\text{1.5}\text{PV}}{\text{R}\left(273\right)}+\frac{\text{1.5}\text{PV}}{\text{R}\left(\text{T}\right)}$
$\Rightarrow \frac{2}{273}=\frac{1.5}{273}+\frac{\text{1.5}}{T}$
$\Rightarrow T=819K=546^{\circ }C$