Question

A tire at 21°C has a pressure of 0.82 atm. Its temperature decreases to –3.5°C. If there is no volume change in the tire, what is the pressure after the temperature change?

Answer 1

The correct answer is A 0.75 atm

Answer 2

Answer : The pressure after the temperature change is, 0.75 atm.

Solution :

According to the Gay-Lussac's Law, the pressure is directly proportional to the temperature of the gas at constant volume and number of moles.

`P\propto T` (At constant volume and number of moles)

Or,

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

where,

`P_1` = initial pressure = 0.82 atm

`P_2` = final pressure = ?

`T_1` = initial temperature =
`21^oC=273+21=294K`

`T_2` = final temperature =
`-3.5^oC=273+(-3.5)=269.5K`

Now put all the given values in the above formula, we get the final pressure of the gas.

`(0.82atm)/(P_2)=(294K)/(269.5K)`

`P_2=0.75atm`

Therefore, the pressure after the temperature change is, 0.75 atm