Question

O2 gas is filled in a cylinder. when pressure is increased 2 times, temperature becomes 4 times. How much times their density will become? ​

Answer 1

let initial pressure of O2 gas = P

final pressure of O2 gas = 2P

similarly, let initial temperature of O2 gas = T

final temperature of O2 gas = 4T

we know, density, d = PM/RT

where M is molar mass of gas and R is universal gas constant.

hence, density is directly proportional to Pressure but inversely proportional to temperature.

i.e., $\frac{d_1}{d_2}=\frac{P_1}{P_2}\frac{T_2}{T_1}$

= (P/2P) × (4T/T)

= 2/1

⇒$d_2=\frac{1}{2}d_1$

hence, density becomes half of initial value.