39.Heat capacity of perfect gas. Mayer’s equation.

The ideal gas heat capacity - the ratio of the heat communicated to the gas, to the temperature change δТ, which in this case has occurred.

For an ideal gas the relation Mayer:

,

where ~ R - the universal gas constant, ~  - molar heat capacity at constant pressure, ~ - molar heat capacity at constant volume.

Mayer equation follows from the first law of thermodynamics applied to the isobaric process in an ideal gas:

,

.

Obviously, the equation Mayer shows that the difference of thermal capacities of gas equal to the work done by one mole of an ideal gas at the temperature change of 1 K, and explains the meaning of the universal gas constant R - mechanical equivalent of heat.

40.Heat capacities in isoprocess.

adiabatic

In an adiabatic process heat exchange with the environment occurs,   .. However, volume, pressure and temperature changes, .

Consequently, the heat capacity of an ideal gas in an adiabatic process is equal to zero:

  .

Isothermal

The isothermal process is constant temperature,   . . If you change the volume of gas transmitted (or selected) some heat. Consequently, the heat capacity of an ideal gas is minus infinity:  

Isochoric

The isochoric process is constant volume, \ .Elementary work is the product of gas volume change in the pressure at which the change occurs ( ).The first law of thermodynamics for isochoric process is as follows:

For perfect gas

where i - the number of degrees of freedom of the gas particles.

Other formulas:

,

where γ - the adiabatic index, R - the universal gas constant.