Answer: The final temperature of the gas is 7.58 °C.
Explanation: We are given initial and final pressure of the system and we need to find the final temperature of the system.
To calculate it, we use the equation given by Gay-Lussac.
His law states that pressure is directly related to the temperature of the gas.
[tex]P\propto T[/tex]
Or,
[tex]\frac{P_1}{T_1}=\frac{P_2}{T_2}[/tex]
where,
[tex]P_1[/tex] = initial pressure = 893 mmHg = 1.175atm (Conversion factor: 1atm = 760mmHg)
[tex]T_1[/tex] = initial temperature = 49.3°C = [49.3 + 273.15]K = 322.45K
[tex]P_2[/tex] = Final pressure = 778mmHg = 1.023atm
[tex]T_[/tex] = Final temperature = ?°C
Putting values in above equation, we get:
[tex]\frac{1.175atm}{322.45K}=\frac{1.023atm}{T_2}\\\\T_2=280.73K[/tex]
Converting Final temperature from kelvin to degree Celsius.
[tex]T_2=280.73K=[280.73-273.15]^oC=7.58^oC[/tex]
Hence, the final temperature of the gas is 7.58 °C.
