Question

Two identical glass bulbs are interconnected by a thin glass tube. A gas is filled in these bulbs at NTP (take temperature as $273$ Kelvin). If one bulb is placed in ice at $0^{\circ }C$ and another bulb is placed inside hot bath, then the pressure of the gas becomes $1.5$ times of initial value. The temperature of hot bath is $91\times n$ in degree celsius , then the value of $n$ is, where $n$ is an integer (take the nearest integer)

Answer 1

Quantity of gas in these bulbs is constant, i.e., initial number of moles in both the bulbs $=$ final number of moles
${\mu }_1+{\mu }_2={\mu }_1^{\prime }+{\mu }_2^{\prime }$

$\frac{PV}{R\left(273\right)}+\frac{PV}{R\left(273\right)}=\frac{1.5PV}{R\left(273\right)}+\frac{1.5PV}{R\left(T\right)}$

$\Rightarrow \frac{2}{273}=\frac{1.5}{273}+\frac{1.5}{T}$

$\Rightarrow T=819K={546}^{\circ }C$

So the value of $n$ is 6.