- #1
physiks
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Using kinetic theory, we can derive an expression for the thermal conductivity of a gas to be
κ=nCmoleculeλ<v>/3
where n is the number density of the molecules in the gas, Cmolecule 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 nCmolecule=CV/V where CV is the heat capacity of the gas at constant volume and V is the total volume of the gas. Now I understand that nCmolecule=C/V where C is the heat capacity of the gas, and obviously because we have a gas we must have either C=CV or C=Cp 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
κ=nCmoleculeλ<v>/3
where n is the number density of the molecules in the gas, Cmolecule 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 nCmolecule=CV/V where CV is the heat capacity of the gas at constant volume and V is the total volume of the gas. Now I understand that nCmolecule=C/V where C is the heat capacity of the gas, and obviously because we have a gas we must have either C=CV or C=Cp 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