### Charles Law

The volume of a fixed mass of gas is directly proportional to its temperature at constant pressure.

Please move the slider and experiment with it.

V ∝ T

v ∝ t

v = k t

v = k t

As you can see, the line, when extended backwards crosses the x-axis at -273 C^{0}. There is a special temperature when all gases have zero volume, called **Absolute Temperature**.

So, 0 T = -273 C

+ 273 => 273 T = 0C

+ t => (273 + t) T = t C

**T = 273 + t**, where t is the temperature in Celsius.

If the temperature and volume of a fixed mass of gas take the values of v_{1} T_{1}and V_{2} T_{2} respectively, where T is absolute
temperature,

V_{1} / T_{1} = V_{2} / T_{2}

**E.g.**

The volume of a fixed mass of air is volume is 8 cm^{3} at 27 C^{0}. Its
temperature is raised to 127 C^{0}, while keeping the pressure constant. Find the volume.

p

_{1}= 20, v

_{1}= 8, p

_{2}= 40

According to Charles's law,

V

_{1}/ T

_{1}= V

_{2}/ T

_{2}

8 / (273 + 27) = v

_{2}/ (273 + 127)

v

_{2}= 10.6cm

^{3}

Please answer the following questions.

- The volume of a gas at 30C
^{0}is 8 cm^{3}. Find its volume when the temperature is 50C^{0}while pressure remains the same. - The volume of a gas at constant temperature is plotted against temperature in Celsius. What do the gradient and intercept represent ?
- The volume of a gas at 30C
^{0}is x cm^{3}. Find x when the temperature is 50C^{0}while pressure remains the same.