Question

The gauge pressure in your car tires is 2.40 x 10^5 N/m^2 at a temperature of 35.0°C when you drive it onto a ferry boat to Alaska. What is their gauge pressure (in atm) later, when their temperature has dropped to −42.0°C? (Assume that their volume has not changed.)

Answer 1

The gauge pressure is
`1.8*10^(5)\ N/m^2`

Step-by-step explanation:

Given that,

Gauge pressure of car tires
`P_(1)=2.40*10^(5)\ N/m^2`

Temperature
`T_(1)=35.0^(\circ)C = 35.0+273=308 K`

Dropped temperature
`T_(2)= -42.0^(\circ)C=273-42=231 K`

We need to calculate the gauge pressure P₂

Using relation pressure and temperature

`(P_(1))/(T_(1))=(P_(2))/(T_(2))`

Put the value into the formula

`(2.40*10^(5))/(308)=(P_(2))/(231)`

`P_(2)=(2.40*10^(5)*231)/(308)`

`P_(2)=180000 = 1.8*10^(5)\ N/m^2`

Hence, The gauge pressure is
`1.8*10^(5)\ N/m^2`