Adiabatic and Isothermal Expansions
The graphs below show how the pressure (y-axis) of a gas falls as its volume increases (x-axis). For both the curves shown the initial conditions are: Temperature= 300 K: Molar density = one mole of gas is held in a volume of 1 litre (0.001 cubic metres): gamma= 1.66 i.e. the gas is a monatomic gas such as Argon

• The red curve corresponds to an isothermal expansion
• The green curve corresponds to an adiabatic expansion
  

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Notice that:

• The initial pressure of the gas (2.5 MPa) corresponds to around 25 times atmospheric pressure. The force exerted by the gas on the walls of its container would be very considerable. For example the force on a 10 cm x 10 cm area would be around 2.5 kN (equivalent to a weight of around 2.5 tonnes) .
• The temperature of 300 K corresponds to a temperature of around 27 celsius.
• In the isothermal expansion, the temperature remains constant.
• In the adiabatic expansion the gas cools during the expansion. This means that at a given volume its pressure will be less than for the isothermal curve.
• The extent of the difference between adiabatic and isothermal curves depends on the value of gamma. The quicktime animation below shows the effect of varying gamma from around 1.66 to 1.00. Physically, varying gamma would correspond to performing the same experiment with different gases, each with a single value of gamma.

Notice that:

• Large values of gamma (around 1.66: slider to the far right) correspond to monatomic gases. Here all the energy for the expansion is drawn from just three degrees of freedom. Each degree of freedom loses a relatively large amount of energy which is converted to work during the expansion.
• Small values of gamma (just greater than 1: slider to the far left) correspond to polyatomic gases. Here the energy for the expansion is drawn from many degrees of freedom and so no particular degree of freedom has to lose as much energy. Thus gases with small values of gamma cool less as they expand adiabatically.

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