If 11.00 mol of helium gas is at 12.0 ∘c and a gauge pressure of 0.400 atm. calculate the temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.

Assuming ideal behavior of the helium gas for a fixed amount, the value of PV/T is constant, that is,

P1V1 = nRT1, P2V2 = nRT2

If the gas is compressed to precisely half the volume and the absolute pressure is equal to gauge pressure plus atmospheric pressure, we rearrange the expression to solve for the temperature:

T2/T1 = (P2/P1) (V2/V1)

T2 = (P2/P1) (V2/V1) T1

T2 = (2.00atm/1.350atm) (1/2) (283K)

T2 = 210 K = - 63°C