In an experiment to simulate conditions within an automobile engine, 0.170 mol o

Question

In an experiment to simulate conditions within an automobile engine, 0.170 mol of air at a temperature of 700 K and a pressure of 3.00×106 Pa is contained in a cylinder of volume 330 cm3 . Then 605 J of heat is transferred to the cylinder

1)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.

T=?

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

T=?

Explanation / Answer

We know,
pv = nRTi
3 * 10^6 * 330 /100^3 = 0.170 * 8.314 * Ti
Ti = 700.44 K

(a)
Heat is added at Constant Volume -
U = Q = n Cv T
Cv = 5R/2
Q = 605 J

605 = 0.170 * 2.5 *R * T
T = 605/(0.170 *2.5*8.314)
T = 171.22

Tf = Ti +  T
Tf = 700 + 171.22 k
Tf = 871.22 k
Final Temperatue of the air Tf = 871.22 k

(b)
Heat is added at Constant Pressure -
U = Q = n Cp T
Cp = Cv +R
Cp = 2.5R +R
Cp = 3.5R

Q = n Cp T
605 = 0.17 * 3.5 * 8.314 *T
T = 605 / (0.17 * 3.5 * 8.314)
T = 122.3 K

Tf = Ti +  T
Tf = 700 + 122.3 k
Tf = 822.3 k
Final Temperatue of the air Tf = 822.3 k

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