Equal masses of air are sealed in two vessels, one of volume V0 and the other of volume 2V0. If the first vessel is maintained at a temperature 300 K and the other at 600 K, find the ratio of the pressures in the two vessels.
We know ideal gas equation
PV=nRT
Where V= volume of gas
R=gas constant
T=temperature
n=number of moles of gas
P=pressure of gas.
Given
Masses of both the gas is equal. Therefore, number of moles of both the gas is equal. So, we can write
n1 =n2 =n
Volume of first gas V1=Vo
Volume of second gas V2=2Vo
Temperature of first gas T1=300K
Temperature of second gas T2=600K
Let pressure of first gas =P1
Pressure of second gas=P2
Applying ideal gas equation for both the gases
P1V1=n1RT1
…(I)
P2V2=n2RT2
…. (II)
Since n1 =n2 =n
Therefore
Rearranging the above equation
P1:P2 =1:1
So, the ratio of pressure gas in two vessels is 1:1.