Question

the temperature of the gas contained in a closed vessel increases by 1C when the pressure of the gas is increased by 1% then the initial temperature of the gas is.... the ans given is 100K but my doubt is temperature and pressure are directly proportional to each other then if pressure is increased by 1% then temperature should be increased by 1% and it is increased by 1C then initially it should be 100C naa...why kelvin?

Answer 1

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

Let T2 = T1 + 1 ... (Note: A 1 degree increase on the Celsius scale is a 1 degree increase on the Kelvin scale. Temperatures used in the combined gas law must be in Kelvin.)

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