Question

the pressure of a gas filled in a closed vessel increases by 2% when temperature is increased by 4°C. What is the initial temperature of the gas?

Answer 1

P α T
⇒ P = kT

P₁ = P
P₂ = 1.02 P
T₁ = T
T₂ = T+4

P₂/P₁ = T₂/T₁
1.02P/P = T+4/T
1.02 = T+4/T
1.02T  = T+4
1.02T - T = 4
0.02T = 4
T = 4/0.02 = 200 K

Initial temperature is 200 kelvin.