Question

An ideal gas in a sealed container has an initial volume of 2.50 L. At constant pressure, it is cooled to 21.00 ∘C, where its final volume is 1.75 L. What was the initial temperature?

Answer 1

Answer: The initial temperature of the system comes out to be 147 °C

Explanation:

To calculate the initial temperature of the system, we use the equation given by Charles' Law. This law states that volume of the gas is directly proportional to the temperature of the gas at constant pressure.

Mathematically,

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

where,

$V_1\text{ and }T_1$ are the initial volume and temperature of the gas.

$V_2\text{ and }T_2$ are the final volume and temperature of the gas.

We are given:

$V_1=2.50L\\T_1=?K\\V_2=1.75L\\T_2=25^oC=(25+273)K=294K$

Putting values in above equation, we get:

$\frac{2.50L}{T_1}=\frac{1.75L}{294K}\\\\T_1=420K$

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

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

$420=T(^oC)+273\\T(^oC)=147^oC$

Hence, the initial temperature of the system comes out to be 147 °C