We have already Pv ^{n}=C

V ^{n} d P + P n v^{ n 1 }dv = 0

dp / du = – n p / u

slope = – n p / u

From there we get that slope depends on P and v for a particular n, in negative sense.

Process | Value of n | Equation of process |

Isobaric Process
Isothermal Process Isentropic Process Isometric or isochoric Process |
n = 0
n = 1 n = y · |
P = Const.
T = Const. S = Const. v = Const. |

Similarly u_{1} = u_{2}

u_{2 }= u_{3} and so on

u = constant for n=∞

**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
- Entropy change of an ideal gas
- Reversible adiabatic process
- P v and t s diagrams for pv c

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