Answer: The percent change in volume will be 25 %
Explanation:
To calculate the final 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,
[tex]\frac{V_1}{T_1}=\frac{V_2}{T_2}[/tex]
where,
[tex]V_1\text{ and }T_1[/tex] are the initial volume and temperature of the gas.
[tex]V_2\text{ and }T_2[/tex] are the final volume and temperature of the gas.
We are given:
[tex]V_1=2L\\T_1=T_1\\V_2=?\\T_2=75\% \text{ of }T_1=0.75\times T_1[/tex]
Putting values in above equation, we get:
[tex]\frac{2L}{T_1}=\frac{V_2}{0.75\times T_1}\\\\V_2=\frac{2\times 0.75\times T_1}{T_1}=1.5L[/tex]
Percent change of volume = [tex]\frac{\text{Change in volume}}{\text{Initial volume}}\times 100[/tex]
Percent change of volume = [tex]\frac{(2-1.5)}{2}\times 100=25\%[/tex]
Hence, the percent change in volume will be 25 %
