On a cool morning, when the temperature is 14°C, you measure the pressure in your car...
On a cool morning, when the temperature is 14°C, you measure the pressure in your car tires to be 26.8 psi. After driving 27 mi on the freeway, the temperature of your tires is 46°C. What pressure will your tire gauge now show?
Homework Answers
pressure P1 =26.8Psi = 26.8*6895Pa = 1.847*10^5 Pa
Temperature T1 = 14C = 14+273 = 287 K
T2 = 46 C = 46+273 = 319 K
from the relation
P1/T1 = P2/T2
P2 = P1T2/T1 = 1.847*10^5*319/287 =2.053*10^5 Pa
P2 = 29.77 Psi
Assuning ideal gas behavior:
P1/P2=T1/T2
Here, P1=26.8 psi
T1=14 ? =287 K
T2=46 ? =319 K
P2=(T2/T1)*P1
=(319/287)*26.8
=29.79 psi
Assume constant volume, gas constant, and mass and use
the Ideal Gas Law to find the Pressure.
PV = m*R*T
V/(m*R) = T/P = constant
T1/P1 = T2/P2
P2 = P1*T2/T1
Remember to use Rankine for temp
T1 = 14 C = 516.87 R
T2 = 46 C = 574.47 R
P2 = 26.8 * 574.47/516.87 = 29.78 psi
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