Answer: The temperature of the gas in the tire if the pressure in the tire increases to 87.3 kPa is [tex]45^0C[/tex]
Explanation:
To calculate the final temperature of the system, we use the equation given by Gay Lussac Law. This law states that pressure of the gas is directly proportional to the temperature of the gas at constant volume.
Mathematically,
[tex]\frac{P_1}{T_1}=\frac{P_2}{T_2}[/tex]
where,
[tex]P_1\text{ and }T_1[/tex] are the initial pressure and temperature of the gas.
[tex]P_2\text{ and }T_2[/tex] are the final pressure and temperature of the gas.
We are given:
[tex]P_1=82.0kPa\\T_1=26.0^oC=(26.0+273)K=299K\\P_2=87.3kPa\\T_2=?[/tex]
Putting values in above equation, we get:
[tex]\frac{82.0}{299}=\frac{87.3}{T_2}\\\\T_2=318K=(318-273)^0C=45^0C[/tex]
Thus the temperature of the gas in the tire if the pressure in the tire increases to 87.3 kPa is [tex]45^0C[/tex]
