a. Suppose 20 percent of an ideal gas is removed from a gas cylinder while its t
ID: 1516044 • Letter: A
Question
a. Suppose 20 percent of an ideal gas is removed from a gas cylinder while its temperature changes by 105 percent (if given percentage of temperature change is positive, assume it increases). If the initial pressure of the gas is Po, what is the final pressure of the gas in terms of Po.
________Po
b. Suppose the gauge pressure of the tire on the front passenger tire is 41.7 psi when the outdoor temperature is 100.0oF. Assuming the volume of air in the tire remains constant, what is the gauge pressure of the tire when the temperature drops to 14.0oF.
__________psi
c. Repeat the question assuming the volume of the tires decreases by 12 percent. How important is it to check the pressure of your car tires when it gets cold outside?
__________psi
Explanation / Answer
a)
P2V2=nRT2 --------------(1)
P1V1=nRT1 --------------(2)
From (1) and (2),
P2V2/P1V1= T2/T1
P2 = (T2P1V1)/(V2T1) = (T2/T1)*(V1/V2)*P1 = (1.05T1/T1)*(V1/0.8V1)*P0 = (1.05)*(1/0.8)*P0 = 1.3125P0
b)
P1= 41.7 psi
T1= 100 oF = 37.78 C
T2 = 14.0 oF
V1=V2
P2V2/P1V1= T2/T1
P2/P1= T2/T1
P2= (T2/T1)*P1 = (14.0/100)*41.7 = 5.84 psi
c)
P1= 41.7 psi
T1= 100 oF = 37.78 C
T2 = 14.0 oF
V2= 0.12V1
P2V2/P1V1= T2/T1
P2= (T2V1P1)/(V2T1) = (14.0/100)*(1/0.12)*41.7 = 48.65 psi
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