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 : 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,
\(\frac{P_1}{P_2}=\frac{T_1}{T_2}\)
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.
\(\frac{0.82atm}{P_2}=\frac{294K}{269.5K}\)
\(P_2=0.75atm\)
Therefore, the pressure after the temperature change is, 0.75 atm