On a cool morning, when the temperature is 13 C, you measure the pressure in your car tires to be 30 psi. After driving 50 mi on the freeway, the temperature of your tires is 42C.
What pressure will your tire gauge now show?
T1 = 13 C
T2 = 42 C
P1 = 30 psi
P2 = ?
By perfect gas equation, as V is constant,
P1V = RT1
P2V = RT2
P2/P1 = T2/T1
P2 = P1xT2/T1
P2 = 30x42/13 = 96.92 psi...what seems to be a problem?
Thanks, I totally forgot about adding 14.7psi
You're supposed to convert celsius to kelvin first, and then work from there.
No.NO. When one measures tire pressure, you measurt gage pressure (realtirepressure-atmosphericpressure)
So for the real tire pressure, add 14.7psi
P1=44.7PSI
P2=?
then subtract 14.7 psi to get P2 gauge pressure.
Finally, Temperatures must be in Kelvins, not C
T1 = 13 C
T2 = 42 C
P1 = 30 psi
P2 = ?
By perfect gas equation, as V is constant.
t1=13+273K = 286K
t2=42+273K=315K
P1=30+14.7 = 44.7
P2=?
P2/P1 = T2/T1
P2 = P1xT2/T1
P2=44.7x315K/286K
P2=49.23atm -14.7=34.5psi
Based on the calculations, the pressure in your tires would be around 96.92 psi after driving 50 miles on the freeway. However, there seems to be a problem with the calculations. The perfect gas equation assumes that the volume (V) and the amount of gas remain constant. In reality, as the tires heat up, the volume and the amount of gas inside them may change, affecting the pressure.
To more accurately calculate the change in pressure, you would need to consider the ideal gas law, which takes into account the changing volume and amount of gas as well. The ideal gas law equation is:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature in Kelvin
To solve for P2, you would need to know the initial volume (V1), the molar amount of gas (n), and the ideal gas constant (R) as well. Without these additional values, it is difficult to accurately determine the pressure (P2) after driving 50 miles on the freeway.