Question

a cylinder of gas is at room temperature (20 °C) the air conditioner breaks down and the temperature rises to 40°C what is the new pressure of gas relative to its initial pressure

Answer 1

Given,

The initial temperature of the room, T₁=20 °C=293.15 K

The final temperature, T₂=40 °C=313.15 K

Let the initial temperature of the room be P₁, and the final temperature be P₂

From Gay-Lussac's law,

`(P_1)/(T_1)=(P_2)/(T_2)`

On substituting the known values in the above equation,

`(P_1)/(293.15)=(P_2)/(313.15)`

Therefore P₂ is given by,

`P_2=(P_1*313.15)/(293.15)=1.07P_1`

Therefore, the new pressure relative to the initial pressure is 1.07 times the initial pressure, i.e., 1.07P₁