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Note that the expression that gives the change in the internal energy of an ideal gas is the same regardless of the process that it undergoes, since the internal energy is a state function. The change in the internal energy of the ideal gas is given by:

This formula can be rewritten as PKV- In order to calculate the work done in adiabatic process, let us consider the system is compressed from the initial position of P1, V1 and T1 to final position P2, V2 and T2. Since point B is located on an isotherm that is below the one which passes through point A, it means that an ideal gas cools down during an adiabatic expansion. The work done in an adiabatic process can be derived from the formula for adiabatic process PV Constant (K). Which is positive since the gas expands when it goes from state A to state B.įrom the figure above, we can also observe that the temperature of the ideal gas is lower in state B than in the initial state A.

The work done by the gas (that corresponds to the shaded area in blue in the PV diagram) is calculated by integrating the expression of the work done by a gas:īy substituting the value of the constant, we get: The following PV diagram shows the adiabatic process as well as the work done by the gas when it goes from state A to state B: That is, the product of the pressure by the volume raised to the heat capacity ratio has the same value for any state of the adiabatic process.Īs the heat capacity ratio is greater than 1, the curve which represents a reversible adiabatic process for a ideal gas has a greater slope (in absolute value) than that of the isotherm of an ideal gas. The quotient C P/C V is called the heat capacity ratio (or adiabatic index) γ.īy integrating the previous equation between any two states A and B, we obtain:įinally, the equation of a reversible adiabatic process of an ideal gas is: To simplify the second member of the equation, we use the Mayer’s relation: Next we can equal both expressions for dT: In addition, the work done by a gas enclosed in a container and the change in the internal energy of an ideal gas are given respectively by:īy substituting in the differential form of the first principle and by isolating, we obtain:īy differentiating the equation of state of an ideal gas we get: First of all we are going to determine the equation that relates the pressure to the volume starting from the differential form of the First Law of Thermodynamics and using the equation of state of an ideal gas.īy definition the heat exchanged in an adiabatic process is zero. The volume, pressure and temperature of the gas varies as it expands. The container is covered with an adiabatic wall. Consider n moles of an ideal gas enclosed in a container with a moving wall (a piston for instance) as shown in the figure below.