## Calculating Internal Energy & Enthalpy of an Ideal Gas

For an ideal gas the change in internal energy and enthalpy can be calculated for a temperature change of that gas. This was discovered when Joule conducted an experimented where one tank contained air at a high pressure, and another tank was evacuated. These tanks were connected to each other by a valve and then placed in a water bath until thermal equilibrium was obtained. After thermal equilibrium was obtained he opened the valve letting air from the higher pressure tank pass into the other tank until the pressures had equalized. After this was done Joule observed that there was no temperature change of the water bath, and concluded that internal energy is a function of temperature. Since internal energy is a function of temperature, for an ideal gas equation 3 can be used to calculate the change in internal energy for a change in temperature.

c_{v} = Specific Heat at Constant Volume

T = Temperature

For an ideal gas, change in enthalpy is also a function of temperature. This can be shown by combining the ideal gas law and the definition of enthalpy. Refer to equation 2.

h = enthalpy

u = internal energy per unit mass

P = Pressure

v = specific volume

R = Ideal Gas Constant

Finally the change in enthalpy for temperature difference of an ideal gas can be calculated using equation 3.

c_{p} = Specific Heat at Constant Pressure

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