## Charles's Law

## What is Charles's Law?

Charles's Law states that the temperature and volume of an ideal gas are directly proportional. This can be represented mathematically

by the equation V = kT. Plotting volume against temperature yields a straight line with y - intercept at 0.

by the equation V = kT. Plotting volume against temperature yields a straight line with y - intercept at 0.

In other words, to calculate the change in volume for temperature after a change in the other variable, the equation could be written as Vinitial / Tinitial = Vfinal / Tfinal.

## Example

A balloon with 750.0 mL of gas at a temperature of 235oC is cooled with the same pressure to a temperature of 50oF. What is the final Volume of the gas in the balloon?

50 °F = 10 °C = 283 °K

235 °C = 508 °K

Using Charles Law:

Vinitial / Tinitial = Vfinal / Tfinal

750 mL /508 °K = x mL / 283 °K

750 mL x 283 °K /508 °K = x mL = 417.815 mL

50 °F = 10 °C = 283 °K

235 °C = 508 °K

Using Charles Law:

Vinitial / Tinitial = Vfinal / Tfinal

750 mL /508 °K = x mL / 283 °K

750 mL x 283 °K /508 °K = x mL = 417.815 mL

Hot Air Balloons and Their Usage of Charles's Law

## Practice Problems

1. A stretchable plastic bag was inflated to 100ml of gas at room temperature (21°C). After the leakage in the bag, there was only 20 ml of gas. What is the temperature of the gas?

2. A hot air ballon with a volume of 2L started at the ground with the flames running. The balloon went from room temperature to a blazing, hot temperature of 150°C. After the flames ran for some time, what was the final volume? (assume that no air was released in the process and the baloon would not blow up)

3. A rubber glove was inflated to reach 1/2 its total stretchability at room temperature (21°C). The rubber glove is said to blow up after it reaches 150% of the maximum stretchability. The rubber glove was heated to 100 °C. Would the rubber glove have blown up?

4.A rubber tire is currently 75% full at 35°C. It is an extremely, hot day and reached 55°C. If the the rubber can only reach a maximum of 105% pressure before exploding, will the tire explode at 55°C.

2. A hot air ballon with a volume of 2L started at the ground with the flames running. The balloon went from room temperature to a blazing, hot temperature of 150°C. After the flames ran for some time, what was the final volume? (assume that no air was released in the process and the baloon would not blow up)

3. A rubber glove was inflated to reach 1/2 its total stretchability at room temperature (21°C). The rubber glove is said to blow up after it reaches 150% of the maximum stretchability. The rubber glove was heated to 100 °C. Would the rubber glove have blown up?

4.A rubber tire is currently 75% full at 35°C. It is an extremely, hot day and reached 55°C. If the the rubber can only reach a maximum of 105% pressure before exploding, will the tire explode at 55°C.