Thermal conductivity and heat capacity

• physiks
In summary: No, the pressure and volume are not fixed.You are assuming the gas is in a steady state.No, the pressure and volume are not fixed.

physiks

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...

physiks said:
why we have to consider the heat capacity at constant volume here
physiks said:
n is the number density
Stick with the original constraints on the calculation.

Bystander said:
Stick with the original constraints on the calculation.

What does this mean?

You started your calculation at constant V. Finish at constant V.

Bystander said:
You started your calculation at constant V. Finish at constant V.

Ok, but I can't see why we started at constant V?

You haven't included any dependence of V on P, T.

Bystander said:
You haven't included any dependence of V on P, T.

Oh I see, so my derivation basically assumes the whole system is in a steady state (transport properties are for steady state systems), because I used a fixed temperature gradient. So then the pressure and volume must be fixed (if the pressure was fixed but volume varied, my temperature would change, so we need to fix volume and pressure).

What is thermal conductivity?

Thermal conductivity is the measure of a material's ability to conduct heat. It is the rate at which heat flows through a material, per unit temperature gradient.

What is the unit of thermal conductivity?

The unit of thermal conductivity is watts per meter Kelvin (W/mK), representing the amount of heat that flows through a material with a thickness of one meter, per degree of temperature difference.

What factors affect thermal conductivity?

The thermal conductivity of a material is affected by its composition, density, and temperature. Materials with higher density and higher thermal conductivity coefficients tend to have higher thermal conductivity.

What is heat capacity?

Heat capacity is the amount of heat energy required to raise the temperature of a substance by one degree Celsius. It is a measure of how much heat a material can store.

What is the difference between thermal conductivity and heat capacity?

Thermal conductivity measures how easily heat can flow through a material, while heat capacity measures how much heat a material can store. In other words, thermal conductivity is a measure of a material's ability to conduct heat, while heat capacity is a measure of a material's ability to store heat.