With volume and molar quantity held constant,by what factor does the absolute temperature change for an ideal gas when the pressure is five times bigger?
A)1/5
B)1
C)5
D)25

Question

Quizplus · Accepted Answer

According to the Ideal Gas Law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is absolute temperature. If volume and the number of moles are held constant, then PV = constant. Thus, we can say that P1V1 = P2V2, where P1 and V1 are the initial pressure and volume and P2 and V2 are the final pressure and volume.

Now we can solve for the changing temperature:

P1V1 = P2V2

T1 = P1V1/nR

T2 = P2V2/nR

T2/T1 = (P2V2/nR)/(P1V1/nR)

T2/T1 = P2/P1

If the pressure is five times bigger (P2 = 5P1), then:

T2/T1 = 5

Thus, the absolute temperature has changed by a factor of 5. Therefore, the answer is C) 5.

With Volume and Molar Quantity Held Constant,by What Factor Does