# Laws Of Thermodynamics…..

Hello Guys…!!

Here is a fast over-view of Laws of Thermodynamics.

Zeroth Law of Thermo dynamics:

Let A, B, C be different bodies having different temperatures. If heat exchange is possible between A and B and B and C then it is also possible between A and C. Work and Heat:

Work:

• It is the mode of energy transfer mechanical work = PΔV = Pext (V₂ – V₁).
• It is a path dependent function
• Work done on system increases the energy of a system and work done by system decreases the energy of system

Heat:

• It is the quantity of heat which flows between system and surrounding.
• Always flows from higher temperature to lower temperature.

Internal Energy:

E = Etranslational + Erotational + Evibrational + Ebonding + …

Summation of all types of energies constitutes to give net internal energy of a particular system.

First law of thermo dynamics:

Energy can neither be created nor be destroyed. It can be only transformed from one form to another.

Total energy of the universe is constant.

Whenever a quantity of one king of energy disappears, an exactly equivalent quantity of energy in some other form must appear.

E₂ = E₁ + q + W

[E₂ – E₁ = q + W]

ΔE = q + W → (First Law)

Enthalpy:

Heat content at constant pressure is called “Enthalpy”.

ΔH = ΔE + PΔV

Heat capacity:

Quantity of heat required to raise the temperature of the system by one degree.

Heat capacity = $$\left( \frac{dq}{dT} \right)$$

Heat capacity at constant volume = $${{C}_{v}}={{\left( \frac{dE}{dT} \right)}_{v}}$$

Heat capacity at constant pressure = $${{C}_{p}}={{\left( \frac{dH}{dT} \right)}_{P}}$$

Cp – Cv = R

Expansion of an Ideal gas:

1. Isothermal expansion:

ΔE = 0 → for isothermal Process

ΔE = q + w → from first law

∴ q = – ω

ΔH = ΔE + PΔV

ΔH = ΔE + nRΔT

∴ ΔH = 0

a) Work done in reversible isothermal process:

Pext = Pgas = P

$$W=\int\limits_{-{{v}_{1}}}^{{{v}_{2}}}{Pdv}$$

$$W=\int\limits_{-{{v}_{1}}}^{{{v}_{2}}}{\frac{nRT}{V}dv}$$

$$W=-nRT\,\ln \left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)$$

b) Work done for irreversible process: W = – Pext (V₂ – V₁)

q = 0

ΔE = q + ω

∴ ΔE = ω for an adiabatic process.

1. PVϒ = Constant
2. TVϒ⁻¹ = Constant
3. PϒT¹⁻ϒ = Constant

Work done for reversible adiabatic process

$$W=\frac{nR}{(\Upsilon -1)}({{T}_{2}}-{{T}_{1}})$$

Work done for irreversible adiabatic process

$$W=-R{{P}_{ext}}\left( \frac{{{T}_{2}}{{P}_{1}}-{{T}_{1}}{{P}_{2}}}{{{P}_{1}}{{P}_{2}}} \right)$$

Second Law of Thermodynamics:

The Second Law of Thermodynamics states that the state of entropy of the entire universe, as a closed isolated system, will always increase over time. The second law also states that the changes in the entropy in the universe can never be negative.

1. Second law of thermodynamics gives rise to the concept of Entropy
2. Entropy (S) -measure of the number of specific ways in which a thermodynamic system may be arranged, commonly understood as a measure of disorder.
$$S=\frac{{{q}_{rev}}}{T}$$ $$\Delta S=n{{C}_{v}}\,\ln \left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)+nR\,\ln \left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)$$

$$n{{C}_{p}}\,\ln \left( \frac{{{T}_{2}}}{{{T}_{1}}} \right)+nR\,\ln \left( \frac{{{P}_{1}}}{{{P}_{2}}} \right)$$

Gibb’s Free Energy (G):

G = H – TS

ΔG = ΔH – TΔS at constant temperature.

Also, dG = Vdp – SdT

At constant temperature, $$\Delta G=nRT\,\ln \left( \frac{{{p}_{2}}}{{{p}_{1}}} \right)$$

Criteria for Spontaneity:

For a spontaneous process, entropy of universe must increase, i.e. ΔSuniv > 0 or ΔG < 0

(i) If ΔH < 0 and ΔS > 0, ΔG is always negative, always spontaneous.

(ii) If ΔH > 0 and ΔS < 0, ΔG is always positive, always non-spontaneous

(iii) If ΔH > 0 and ΔS > 0, process will be spontaneous higher temperature but non-spontaneous at lower temperature.

(iv) If ΔH < 0 and ΔS < 0, process will be spontaneous lower temperature but non-spontaneous at higher temperature.