CONCEPTUAL: isothermic expansion

[lackos]

I was wondering about the first law of thermodynamics and isothemic expansion. Is there an increase in the the total internal energy of a gas through this process. If not is there a way to calculate heat (i can calculate work) through this process as both pressure and volume vary.

Also is an isothermal expansion the only time when you can use W=-nRT$\intV.dV$.
or can you use that for say an adiabatic expansion where temperature varies

lackos

 

[Andrew Mason]

I was wondering about the first law of thermodynamics and isothemic expansion. Is there an increase in the the total internal energy of a gas through this process. If not is there a way to calculate heat (i can calculate work) through this process as both pressure and volume vary.

It depends on the gas. If it is an ideal gas, the internal energy is proportional to temperature, so there is no change in internal energy during an isothermal process. If it is a non-ideal gas, expansion will result in an increase in potential energy of the molecules (for most non-ideal gases) and therefore will increase internal energy.

Also is an isothermal expansion the only time when you can use $W=-nRT\intV.dV$.
or can you use that for say an adiabatic expansion where temperature varies

I think you meant: $W=-nRT\int dV/V$ where W is the work done ON the gas. I prefer to use W as the work done BY the gas. This is true only for isothermal processes for an ideal gas.

$W = \int PdV$ where W is the work done BY the gas. This is always true. And since for an ideal gas P = nRT/V, $W = \int nRTdV/V$

For isothermal processes, $\int PdV = nRT\int dV/V$ since T is constant.

For an adiabatic process, $\int dW = -\int dU = -\int nC_vdT = -nC_v\Delta T$

AM