Thermodynamics

Thermodynamics


Internal energy : (U)
U = PE + KE of molecules.
Where KE of molecule = (f = degree of freedom & K is Boltzmann constant) and PE of molecules depends upon intermolecular distance (r_o).
Zeroth law of thermodynamic :
If the bodies are in thermal equilibrium with a third body separately, then those two bodies are in thermally in equilibrium with each other.


First law of Thermodynamics :
The amount of heat supplied to a system (dQ) capable of doing external work is equal to sum of increase in the internal energy (dU) and external work done by system (dW)
dQ = dU + dW.
dQ = +ve when heat supplied = - ve when heat rejected dU = +ve when temperature increases = -ve when temperature decreases dW = +ve when work is done by system.
= - ve when work is done on system.

Specific heats of gases :
Amount of Heat required to raise the temperature of whole system by 1°C is Heat capacity of a gas (C)

Cv molar specific heat of gas at constant volume.
Cv specific heat of a gas as constant volume.
Cp molar specific heat of gas as constant pressure.
Cp specific heat of gas at constant pressure units of Cp and C_vare J/mole/k units of Cp and C_vare J/kg/k Cp > C_v
Relation betwen Specificheats of the gas
a) C_p- C_v = r = C_p, C_vSpecificheats per unit mass of gas
b) C_p- C_v= R
R - universal gas constant.
Ratio of specific heats =
As atomicity of gas increases, value of decreases
For MAG - =
For DAG -
For TAG -


Cp & Cv interms of

Number of degrees of freedom does a gas posses is



Isothermal Process:
When a thermodynamic system undergoes a physical change in such a way that its temperature remains constant then the change is known as isothermal changes.
It follows Boyle's law. P₁V₁ = P₂V₂.
During isothermal change, internal energy remains constant. U is constant
du = 0 dQ = dW = pdV
Ex. Melting of ice, Boiling of a liquid are isothermal changes.


Adiabatic process :
When a thermodynamics system undergoes a physical change is such a way that no. exchange of heat takes place between system and surroundings the process is known as adiabatic process.
During adiabatic process, entropy remains constant. Hence it is also known as isoentropic process.
In adiabatic process, dQ = 0
du + dW = 0 du = - dW
In an adiabatic process



Work done in an adiabatic process is given by W =


Second law of Thermodynamics :
Kelvin statement : It is impossible to extract work from a system by cooling it below surrounding temperature. It is impossible to transfer heat energy from body at lower temperature to body at higher temperature unaided by external agency.
Carnot's reversible cycle: It is a reversible engine which absorbs a heat 'Q ' from a source maintained at a constant high temperature 'T₁' K and rejects a heat 'Q₂' to a sink, which is maintained at a constant low temperature 'T₂'K. The efficiency '' of this engine is given by :
.

T₂ temp. of sin k, T₁ temp. of source.

Note : All isothermal and adiabatic changes are reversible if they are performed very slowly.


Refrigerator
(i) A refrigerator is a reversible engine operating in the reverse direction.
In refrigerator, an amount of heat Q₂ is removed from sink at lower rejected at higher temperature T₁to the source.

Thus, Q₂+ W = Q₁ or W = Q₁- Q₂.

(ii) Coefficient of performance. It is defined as the ratio of amount of heat removed from Sink to the amount of work done in removing it. It is denoted by ''
=

Entropy is a measure of disorder of molecular motion of a system. Greater is the disorder, greater is the entropy
dS = or dS =
It is also called second law of thermodynamics.