Question

A tungsten light bulb is usually filled with some inert gases to a pressure of80 kPa at a temperature of 20 °C. The maximum internal pressure that thebulb can withstand is about 280 kPa. Find the temperature in °C of thegases at which the bulb bursts.

Answer 1

Given:

The initial pressure of the gas is,

$P_1=80\text{ kPa}$

The initial temperature is,

$T_1=20+273=293\text{ K}$

The final pressure is,

$P_2=280\text{ kPa}$

Let the final temperature be,

$T_2$

We know,

$\begin{gathered} \frac{P_1}{T_1}=\frac{P_2}{T_2} \\ T_2=\frac{P_2T_1}{P_1} \end{gathered}$

Substituting the values we get,

$\begin{gathered} T_2=\frac{280\times293}{80} \\ T_2=1025\text{ K} \\ T_2=1025-273=752^{\circ}C \end{gathered}$

Hence the required temperature is 752 degrees celcius.