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.

Question

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?

Answer 1

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

Answer 2

Thanks, I totally forgot about adding 14.7psi

Answer 3

You're supposed to convert celsius to kelvin first, and then work from there.

Answer 4

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