**Original equation for entropy change:**

First of all we will consider ds = du / t + pu /t

= cu dt / t + R du / u from equation of 9.3 and then coming to Entropy change between state 1 – 2 :

= ^{2}ʃ_{1} ds = ^{2}ʃ_{1 }c_{v}dT/ T + ^{2}ʃ_{1 }R dv/v

Or, s_{2} – s_{1} = c_{2} In T_{2} / T_{1} + R In v_{2} /v1

we also have Tds = dh udp

ds = dh / T– udp /T

= c_{p}dt / t – R dp /p

**Equivalent equations for entropy change:**

Entropy change between two states 1 – 2 can also be written as

s_{2} – s_{1} = cp In T_{2} / T_{1} –R In P_{2} / P_{1}

As c_{p} – c_{u} = R, equation (9 .19) can be written as

s_{2} – s_{1} = cp In T_{2} / T_{1 }– cp In P_{2} P_{1} + c_{2} In P_{2} / P_{1}

Or, s_{2} –s_{1} = cp In P_{1} T_{1} / P_{2} T_{2} + c_{2} In P_{2} / P_{1}

Also, s_{2} – s_{1} = cp, in v_{2} / v_{1} + c_{2}In p_{2} / p_{1}

Or, s_{2} – s_{1} = cp, in v_{2} / v_{1} + cv In p_{2} / p_{1}

_{ }We can use equations (9.18), (9.19), (9.20) for computing the e::1tropy change betweentwo states of an ideal gas.

**Links of Previous Main Topic:-**

- Open system and control volume
- Conversion of work into heat
- Introduction to carnot cycle
- Clausius inequality entropy and irreversibility introduction
- Ideal gas or perfect gas
- Ideal gas or perfect gas
- Specific heats internal energy and enthalpy of an ideal gas

**Links of Next Mechanical Engineering Topics:-**

- Reversible adiabatic process
- P v and t s diagrams for pv c
- Equations of state
- Law of corresponding states
- Introduction about air standard cycles
- Properties of pure substances introduction
- Vapour compression refrigeration cycle introduction
- Basic fluid mechanics and properties of fluids introduction
- Fluid statics introduction
- Manometers measurement pressure