Question

The gauge pressure in your car tires is 2.50×105N/m2 at a temperature of 35.0°C when you drive it onto a ship in Los Angeles to be sent to Alaska. What is their gauge pressure on a night in Alaska when their temperature has dropped to −40.0°C ? Assume the tires have not gained or lost any air.

Answer 1

Answer:
`1.644* 10^(5) Pa`

Step-by-step explanation:

Given

Initial Gauge Pressure
`P_i=2.50* 10^5 N/m^2`

`P_1_(abs)=(2.50+1.01325)* 10^5`

Temperature
`T_i=35^(\circ)C\approx 308 K`

Final Temperature
`T_f=-40^(\circ)C\approx 233 K`

Also change in volume =0 i.e.
`\Delta V=0`

using
`(P_1V_1)/(T_1)=(P_2V_2)/(T_2)`

`(P_1)/(T_1)=(P_2)/(T_2)`

`((2.50+1.01325)* 10^5)/(308)=(P_f)/(233)`

`P_f=2.65* 10^(5) Pa`

`P_f_(gauge)=2.65-1.01325=1.644* 10^(5) Pa`