Question

In an experiment to simulate conditions within an automobile engine, 0.160 mol of air at a temperature of 740 K and a pressure of 3.30×10⁶ Pa is contained in a cylinder of volume 300cm3 . Then 670 J of heat is transferred to the cylinder.

A) If the volume of the cylinder is constant while the heat is added, what is the final temperature of the air? Assume that the air is essentially nitrogen gas.

B) If instead the volume of the cylinder is allowed to increase while the pressure remains constant, find the final temperature of the air.

Answer 1

apply ideal gas equation as PV = nRT

so initially T1 = PV/nR

T1 = (3.3 e 6 * 300 e-6)/(0.160 * 8.314)

T1 = 744.22 K

part A: At constant Volume, if heat is added , then dU = Q = n CVDT

Cv = 5R/2

so dT = Q/nCV

dT = 670*2 /(0.160 * 5*8.314) = 201.4 deg K

as dT = T2-T1 = 201.4

T2 = 201.4 + 744.22

T2 = 945.6 K

--------------------------------------------------

(b) Heat is added at Constant Pressure dU = Q = n Cp dT

as Cp - Cv = R , Cp = 2.5R +R = 3.5 R

dT = Q/nCp = (670)/(3.5 * 8.314 * 0.16)

dT = 144 deg K

so T2-T1 = 144 K

T2 = 744.22 + 144.4

T2 = 888.63 deg K