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κ=nC

_{molecule}λ<v>/3

where n is the number density of the molecules in the gas, C

_{molecule}is the heat capacity of a single molcule (i.e the heat that must be given to each molecule to raise the temperature of the gas by unit temperature), λ is the mean free path and <v> is the mean speed of the molecules.

Now we can write nC

_{molecule}=C

_{V}/V where C

_{V}is the heat capacity of the gas at constant volume and V is the total volume of the gas. Now I understand that nC

_{molecule}=C/V where C is the heat capacity of the gas, and obviously because we have a gas we must have either C=C

_{V}or C=C

_{p}because the gas must be held at either constant volume or constant pressure. However, I am not sure sure how to see why we have to consider the heat capacity at constant volume here - why can't it be constant pressure...

Thankyou for any answers in advance