#### First Law - Closed Systems: Screencasts

Introduces the first law for a closed system and considers cases of constant pressure and constant volume.

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Applies the first law to a closed system for an adiabatic reversible process for an ideal gas.

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##### Important Equations:

Energy Balance (ignoring kinetic and potential energy):

\[\Delta U = Q + W_{EC} + W_S\]

where \(Q\) is the heat added to the system

\(W_{EC}\) is the expansion/compression work (moving a piston in a cylinder)

\(W_S\) is shaft work

For most processes of importance in chemical engineering, kinetic and potential energies can be ignored.

Adiabatic/reversible compression/expansion for an ideal gas:

\[\frac{T_2}{T_1} = \left( \frac{P_2}{P_1}\right) ^\frac{R}{C_P}\]

where \(T_1\) and \(T_2\) are the absolute temperatures of the gas at the initial and final states, respectively

\(P_1\) and \(P_2\) are the initial and final pressures, respectively

\(R\) is the ideal gas constant

\(C_P\) is the heat capacity at constant pressure

Heat added to the system: \(Q > 0\)

Heat removed from the system: \(Q < 0\)

Adiabatic system: \(Q = 0\)

Work added to the system: \(W > 0\)

Work removed from the system: \(W < 0\)