The specific heat capactity of a particle is the amount of energy needed to raise the temperature of 1kg of the substance by 1K. It can be found using: ΔE = mcΔθ
In a gas, not all particles have the same speed. They have a speed distribution. As the temperature of the gas increases the average particle speed increases and the maximum particle speed increases. Also the distribution curve becomes more spread out.
Energy is transfered between particles through collisions. Some particles will gain speed, and others will slow down. Between collision particles travel at constant speeds. The total energy of the system does not change and so the average speed will stay the same as long as the temperature stays constant.
The internal energy = KE + PE
The average kinetic energy of an individual particle = 1/2mc^2
1/2mc^2 = 3/2 nRT / N
So a rise in temperature will cause a increase in KE and so a higher internal energy
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