We use the ideal gas law, PV = nRT. Since in this example (nR) is a constant value, we can express the ideal gas law in the following way:
PV = nRT
PV/T = nR = constant.
Now, we can further manipulate the law and equate the following:
P1V1/T1 = P2V2/T2 (Combined gas law)
You can use this type of equation not just for constant n problems but for constant T, constant V and constant P problems. In this problem, only n and R remain constant.
In the combined gas law, x1 refers to initial x and x2 refers to final x.
P1 = 0.987 atm (standard pressure)
V1 = 45 litres
T1 = 273.15 K (standard temperature)
P2 = 50 psi = 3.4 atm
V2 = 38 litres
T2 = unknown
Substituting into the combined gas law equation:
(0.987*45/273.15) = (3.4*38/T2)
0.1626 = 129.2/T2
T2 = 129.2/0.1626
= 794.58 K
Been years since I've done this but that result is accurate with experimental observations i.e. temperature of a gas is observed to increase with increasing pressure and decreasing volume.