Respuesta :
Answer: The final temperature of the gas is -220.6°C
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 pressure.
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=6atm\\T_1=-33^oC=[273-33]K=240K\\P_2=1.31atm\\T_2=?[/tex]
Putting values in above equation, we get:
[tex]\frac{6atm}{240K}=\frac{1.31atm}{T_2}\\\\T_2=\frac{1.31\times 240}{6}=52.4K[/tex]
Converting the temperature from kelvins to degree Celsius, by using the conversion factor:
[tex]T(K)=T(^oC)+273[/tex]
[tex]52.4=T(^oC)+273\\\\T(^oC)=-220.6^oC[/tex]
Hence, the final temperature of the gas is -220.6°C
