Question

If the pressure of a gas contained in a closed vessel is increased by 0.4% when heated by 1°C it's initial temperature must be??

Answer 1

As vessel is closed , so volume of the container is constant.

P proportional to T
where P = pressure
and T= temperature

so,
P1/P2 = T1/T2

now pressure in increased by 0.4%
now see in image

so,
solving
we get,
T2=(-23°cescius)
or
T2=250 Kelvin

Answer 2

Let P2 = 1.004 P1 ..... A 0.4% increase in P

Let T2 = T1 + 1 ........... See note below

P1V1/T1 = P2V2/T2 ..... combined gas law

P1/T1 = P2/T2 ............... Assume V remains constant.

T1 = P1T2 / P2 .............. solve for T1

T1 = P1(T1+1) / (1.004P1)

T1 = (T1+1) / 1.004

1.004T1 = T1 + 1

1.004T1 - T1 = 1

0.004T1 = 1

T1 = 1 / 0.004

T1 = 250K

Note: A 1 degree increase on the Celsius scale is a 1 degree increase on the Kelvin scale. Temperatures used in the