# CONCEPTUAL: isothermic expansion

• lackos
In summary: To summarize, the first law of thermodynamics and isothermal expansion depend on the gas being ideal or non-ideal. For ideal gases, there is no change in internal energy during isothermal expansion, but for non-ideal gases, there is an increase in potential energy of the molecules and therefore an increase in internal energy. The equation W=-nRT\int dV/V is only true for isothermal processes for an ideal gas, while W=\int PdV is always true. For adiabatic processes, the equation is -\int nC_vdT = -nC_v\Delta T.
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

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lackos said:
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

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## 1. What is isothermic expansion?

Isothermic expansion is a thermodynamic process in which the temperature of a gas or fluid remains constant while its volume increases.

## 2. How does isothermic expansion differ from adiabatic expansion?

In isothermic expansion, the temperature remains constant, while in adiabatic expansion, there is no heat exchange with the surroundings. This means that in isothermic expansion, the internal energy of the system remains constant, while in adiabatic expansion, the internal energy may change.

## 3. What are the applications of isothermic expansion?

Isothermic expansion is commonly used in refrigeration and air conditioning systems, as well as in heat engines such as steam turbines and internal combustion engines.

## 4. What is the ideal gas law and how is it related to isothermic expansion?

The ideal gas law, PV=nRT, describes the relationship between pressure, volume, temperature, and number of moles for an ideal gas. In isothermic expansion, the temperature remains constant, so the ideal gas law can be simplified to PV=constant. This means that as the volume increases, the pressure must decrease and vice versa.

## 5. How is isothermic expansion represented on a pressure-volume graph?

On a pressure-volume graph, isothermic expansion is represented by a horizontal line, as the pressure and volume remain constant. This line is known as an isotherm and is often used to illustrate the relationship between pressure and volume for a gas at a constant temperature.

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