Question

A gas is confined to a steel tank with a fixed volume . At 293 K, the gas exerts a pressure of 8.53 atm. After heating the tank , the pressure of the gas increases to 10.4 atm. What is the temperature of the heated gas?

Answer 1

Answer: The temperature of the heated gas is 357 K

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,

$\frac{P_1}{T_1}=\frac{P_2}{T_2}$

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:

$P_1=8.53atm\\T_1=293K\\P_2=10.4atm\\T_2=?$

Putting values in above equation, we get:

$\frac{8.53}{293K}=\frac{10.4}{T_2}\\\\T_2=357K$

Hence, the temperature of the heated gas is 357 K