Charles’ Law

discovered by discovered by French French physicist, physicist, Jacques Charles Jacques Charles in 1787in 1787

first person to first person to fill balloon with fill balloon with hydrogen gas hydrogen gas and make solo and make solo balloon flightballoon flight

Charles’ LawCharles’ Law

Temperature vs. VolumeTemperature vs. Volume

If P is constant, gases expand when If P is constant, gases expand when heated.heated.

When T increases, gas molecules move When T increases, gas molecules move faster and collide with the walls more faster and collide with the walls more often and with greater force.often and with greater force.

To keep the P constant, the V must To keep the P constant, the V must increase. increase.

Charles’ LawCharles’ Law states that the states that the volume of a fixed mass of gas volume of a fixed mass of gas varies directly with temperature varies directly with temperature at a constant pressure. at a constant pressure.

V = kT or k = V/TV = kT or k = V/T

k is a constant for a certain k is a constant for a certain sample of gas that depends on sample of gas that depends on the mass of gas and its pressure.the mass of gas and its pressure.

What kind of graph is V vs. T?What kind of graph is V vs. T?

Charles’ Law: T and VCharles’ Law: T and V

Charles’ LawCharles’ Law

If we have a set of new If we have a set of new conditions for the same conditions for the same sample of gas, they will sample of gas, they will have same k so:have same k so:

V1/T1 = k = V2/ T2

V1/T1 = V2/ T2

If we use the Celsius If we use the Celsius temperature system, temperature system, we could end up with we could end up with negative values when negative values when using Charles’ gas using Charles’ gas law.law.

PROBLEM…PROBLEM…

To use Charles’ Law we need a To use Charles’ Law we need a temperature scale that has no temperature scale that has no negative values; this is the negative values; this is the Kelvin Temperature Scale.Kelvin Temperature Scale.

starts at -273.15 ° C = starts at -273.15 ° C = absolute zeroabsolute zero = 0 Kelvin (K) = 0 Kelvin (K)

The lowest possible The lowest possible temperature for this system is temperature for this system is zero.zero.

SOLUTION…SOLUTION…

Example: Charles’ LawExample: Charles’ Law

A gas with a volume of 600 mL has a temperature of 30 0C. At constant pressure the gas is heated until the gas expands to 1,200 mL. What is the new temperature of the gas if the pressure remains constant?

SOLUTIONSOLUTION

1. The first step is to convert the temperature from Celsius to Kelvin: 273 + 30 = 303 K

2. Rearrange Charles’ law to solve for the new temperature: T2= V2 T1 / V1

3. T2 = 1200mL X 303 K = 2 X 303K = 600mL

4. T2 = 606K