Question

a vessel contains 5.0 ft 3 of water at 40 degress and atmospheric pressure. If the water is heated to 80 degress what will be the percentage change in its volume

Answer 1

Answer: The percentage change of volume is 12.8 %

Explanation:

To calculate the final volume 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:

$V_1=5.0ft^3\\T_1=40^oC=(40+273)K=313K\\V_2=?ft^3\\T_2=80^oC=(80+273)K=353K$

Putting values in above equation, we get:

$\frac{5.0ft^3}{313K}=\frac{V_2}{353K}\\\\V_2=\frac{5.0\times 353}{313}=5.64ft^3$

To calculate the percentage change of volume, we use the equation:

$\%\text{ change in volume}=\frac{V_2-V_1}{V_1}\times 100$

Putting values in above equation, we get:

$\%\text{ change in volume}=\frac{(5.64-5.0)}{5.0}\times 100\\\\\%\text{ change in volume}=12.8\%$

Hence, the percentage change of volume is 12.8 %