Chapter 13, Problem 57A

To determine

Height of the piston at $100°C$ .

Answer to Problem 57A

27 cm

Explanation of Solution

Given:

Initial height, $h_1=20cm$, Initial temperature, $T_1=0°C$;After changing this value in kelvin $T_1=273K$

Secondary temperature, $T_2=100°C$; After changing this value in kelvin $T_2=373K$

Formula used:

According to the Charles’ Law, the volume of a gas at constant pressure increases (or rises) linearly with the absolute temperature of the gas. Mathematical expression: $\frac{V_1}{T_1}=\frac{V_2}{T_2}$

Where, $V_1$ is initialvolume, and $V_2$ is final volume, $T_1$ is initialtemperature, and $T_2$ is final temperature.

The height of the piston is directly proportional to the volume of the cylinder:

  $\frac{h_1}{T_1}=\frac{h_2}{T_2}or{h}_2=\frac{h_1{T}_2}{T_1}$

Where, $h_1$ is initial height, and $h_2$ isfinal height, $T_1$ isinitialtemperature, and $T_2$ is final temperature.

Calculation:

Apply the formula, $h_2=\frac{h_1{T}_2}{T_1}$ , and put the given values:

  $\begin{array}{l}{\text{h}}_{\text{2}}\text{=}\frac{\text{(20}\text{cm)(373}\text{K)}}{\text{273}\text{K}}\\ {\text{h}}_{\text{2}}\text{=27}\text{cm}\end{array}$

Conclusion: Hence, height of the piston at $100°C$ is $27cm$ .