Question

At a temperature of -33 degree Celsius, a sample of gas exerts a pressure of 53.3 kPa. At what temperature will the pressure reach 133 kPa?

Answer 1

Answer: The final temperature of the gas is 325.8°C

Step-by-step 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,

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

where,

`P_1\text{ and }T_1` are the initial pressure and temperature of the gas.

`P_2\text{ and }T_2` are the final pressure and temperature of the gas.

We are given:

`P_1=53.3kPa\\T_1=-33^oC=[-33+273]K=240K\\P_2=133kPa\\T_2=?`

Putting values in above equation, we get:

`(53.3kPa)/(240K)=(133kPa)/(T_2)\\\\T_2=(133* 240)/(53.3)=598.9K`

Converting the temperature from kelvins to degree Celsius, by using the conversion factor:

`T(K)=T(^oC)+273`

`598.9=T(^oC)+273\\\\T(^oC)=325.8^oC`

Hence, the final temperature of the gas is 325.8°C