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§4 I law of thermodynamics, Q, U, A to izoprocesses


  1. Isothermal process T = const, m = const.

Boyle's law



ie the total amount of heat imparted to the gas is consumed in the performance of his work against external forces

that at work expanding the temperature did not change to gas during the isothermal process is necessary to sum up the amount of heat equivalent to the work of foreign expansion.

  1. Isobaric process. p = const m = const


Of Mendeleev-Clapeyron equation for state 1 and 2:



The physical meaning of R: R is numerically equal to the work by heating 1 mole of gas at 1K (T2 - T1 = 1 K) in the isobaric process.

heat supplied to the gas, is the change in its internal energy and the work of the commission

  1. Isochoric process

V = const, m = const



All the warmth imparted by gas, is the change in its internal energy.


§ 5 The adiabatic process.

Polytropic process


Called adiabatic process that takes place without heat exchange with the environment. To

 include all the adiabatic fast processes. For example, an adiabatic process can be regarded as

the propagation of sound in the medium, as speed of sound is so high that the energy exchange between the wave and the medium does not have time to happen. Adiabatic processes are used in internal combustion engines, refrigeration, etc. We find the equation relating the parameters of ideal gas at an adiabatic process.

We write I law of thermodynamics.

For an adiabatic process

ie external work is done by changing the internal energy of the system

From equation Mendeleev-Clapeyron express p

Rewritten as:



- Adiabatic equation in the coordinates T and V.


- The Poisson equation (adiabatic equation in the coordinates p and V):

 - the adiabatic (or Poisson's ratio).

pV = const - isotherm equation as γ > 1, the adiabatic curve is steeper than the isotherm. This is explained by the fact that the adiabatic compression 1 - 3 increase in gas pressure due not only to a decrease in its volume as an isothermal compression, but also increase in temperature

- adiabatic equation in the coordinates p, T.

Compute the work is done by the gas in an adiabatic process.

I law of thermodynamics for an adiabatic process

If the gas adiabatically expands from volume V1 to V2, its temperature decreases from T1 to T2, and the work of expansion of ideal gas




The work done by the gas during the adiabatic expansion 1- 2  is equal to square, shaded in the figure and it is less than the work of an isothermal expansion. This is explained by the fact that the adiabatic expansion cools the gas, whereas the isothermal expansion temperature is kept constant by the influx from the outside of the equivalent amount of heat.

Considered isochoric, isobaric, isothermal and adiabatic processes have in common - they occur at constant heat capacity (CV, CP, CT = ∞, CA = 0). In the first two processes are equal to the heat capacity Cv and Cp in an isothermal process (dT = 0) CT = ∞, in an adiabatic process δQ = 0 and CA = 0.

The process in which heat is constant is called polytropic (C = const). Started on the basis of I law thermodynamics at a constant heat capacity (C = const) can be derived polytropic equation


n - adiabatic index.

When C = 0    n = γ     pvγ=const  adiabatic equation

When C = ∞   n = 1    pV = const - isotherm equation

When С = Ср      n = 0    p = const,  

 isobar equation

When С = СV       n = ±  

Thus, all the processes are special cases of a polytropic process.

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