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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 = P
_{ext}(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 = E_{translational} + E_{rotational} + E_{vibrational} + E_{bonding} + …

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 = \({{C}_{p}}={{\left( \frac{dH}{dT} \right)}_{P}}\)

C_{p} – C_{v} = 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:

P_{ext} = P_{gas} = P

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

\(W=-nRT\,\ln \left( \frac{{{V}_{2}}}{{{V}_{1}}} \right) \)b) Work done for irreversible process: W = – P_{ext} (V₂ – V₁)

**2. Adiabatic process:**

q = 0

ΔE = q + ω

∴ ΔE = ω for an adiabatic process.

**Important results for adiabatic process:**

- PV
^{ϒ}= Constant - TV
^{ϒ}⁻¹ = Constant - P
^{ϒ}T¹⁻^{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.

- Second law of thermodynamics gives rise to the concept of Entropy
- Entropy (S) -measure of the number of specific ways in which a thermodynamic system may be arranged, commonly understood as a measure of disorder.

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

**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. ΔS_{univ} > 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.