# Unit 5 Section 2 Energy and Temperature

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## Speed Distribution of Gas Molecules

-The speed distribution of gas molecules depends on the temperature.
-The molecules in a gas do not all travel at the same speed.
-Some molecules will be moving fast but others will be moving much more slowly.
-Most will travel around the average speed.
-The shape of the speed distribution depends on the temperature of the gas.

As the temperature of the gas increases:
-The average molecule speed increases.
-The distribution curve becomes more spread out.

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## Energy Changes Between Molecules

-The molecules of a gas collide with each other all the time.

-Some collisions will be either 'head-on' (molecules moving in opposite directions) or as 'shunts from behind' (molecules moving in the same direction).

-As a result of these collisions energy will be transferred between molecules.

-Some molecules will gain speed in a collision and others will slow down.

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## Heat Transfer

-In particle terms, the particle with more energy transfers some energy to the particle with less energy.

-The higher the difference in temperature between two substances, the faster the heat transfer between substances will happen.

-Heat is also transferred by radiation, and hotter substances radiate heat quicker than cooler substances.

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## Average Kinetic Energy of Gas Molecules - Part 1

1. Ideal gas equation is:

• pV = nRT

2. Equation given by kinetic theory is:

• pV=1/3 x N x m x (Crms)^2

3. Equating these two equations gives:

• 1/3 x N x m x (Crms)^2 = nRT
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## Average Kinetic Energy of Gas Molecules - Part 2

4. Multiplying by 3/2 gives:

• 3/2 x (1/3 x N x m x (Crms)^2 = 3nRT/2

5. 1/2 x m x (Crms)^2 = 3/2 x nRT/2N

6. 1/2 x m x (Crms)^2 = 3/2 x K x T

7. 1/2 x m x (Crms)^2 = 3/2 x RT/NA

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## Total Kinetic Energy of Gas Molecules

Once you have found the averege kinetic energy of the molecules, you can calculate the total kinetic energy of the molecules as long as you know how many molecules there are.

Just multiply the average kinetic energy by the total number of molecules present.

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## Specific Heat Capacity

Specific Heat Capacity: The amount of energy needed to raise the temperature of 1 kg of a substance by 1 K.

Energy change = Mass x Specific Heat Capacity x Change In Temperature

Q = m x c x /\T

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## Specific Latent Heat

Specific Latent Heat: of fusion or of vaporisation is the quantity of thermal energy required to change the state of 1 kg of a substance.

Energy change = Mass of substance changed x Specific Latent Heat

Q = m x l

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