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### Thermodynamics System

#### a) Open system

#### b) Closed System

#### c) Isolated System

### Thermodynamics Process

#### 1) Isothermal Process

#### 2) Isochoric process

#### 3) Isobaric process

The process in which pressure remains constant is called the isobaric process.

#### 4) Adiabatic process

The process in which pressure, volume, and temperature change but the amount of heat remain constant is called the adiabatic process.

**Work done by expansion**

** Fig: Work done by expansion **

Let us consider a gas kept inside a cylinder provided with a movable and frictionless piston at pressure ‘p’, volume ‘v’, and temperature ‘T’. Suppose the gas expands by a small volume ‘dv’ and the piston moved forward by distance ‘dx’. If A is the cross-sectional area of the cylinder then force on the piston,

F = P.A [∴ P=F/A]

Also, the change in volume

dv = Adx

Now,

dw= F.dx

dw= PAdx

dw= Pdv

which is external work done

### PV diagram

### Internal energy

For Ideal gas, Internal energy = kinetic energy

### First Law of thermodynamics

It states that if a certain amount of heat is supplied to the given system then a part of the heat may be used to increase the internal energy and the remaining part is used for work done.

If dQ is the amount of heat supplied to the system and du, dw is the increases in internal energy and external work done respectively, then according to the first law of thermodynamics.

dQ = du + dw — (i)

since

dQ = du + pdv

If dv = 0 then dw = 0

∴ dQ = du

It means the total amount of heat supplied is used to increase external work done only when the volume is constant.

### Heat Capacity of gas

#### Molar heat as constant volume (Cv)

It is defined as the amount of heat required to rise the temperature of 1 mole of gas through 1 kelvin at constant volume. It is denoted by Cv.

#### Molar heat as constant pressure (Cp)

It is defined as the amount of heat required to rise the temperature of 1 mole of gas through 1 kelvin at constant pressure. It is denoted by Cp.

**Mayer’s formula (Cp-Cv=R)**

Let us consider ‘n’ mole of gas kept in a cylinder provided with the movable and frictionless piston at pressure ‘P’, volume ‘V’, and Temperature ‘T’. Suppose the gas is heated at constant volume initially and dQ is the amount of heat given to the system to increase its temperature by dT then,

dQ = nCvdT — (i)

From the first law of thermodynamics,

dQ = du + PdV

Since, at constant volume, dv=0

so, dQ = du

∴ du = nCv dT — (ii)

Again the gas is heated at constant pressure and dQ be the amount of heat given to the system to increase the temperature by dT.

dQ = nCpdT — (iii)

Again from first law of thermodynamics

dQ = du + Pdv

nCpdT = nCvdT + Pdv—(iv) ∴using equation (ii)

From idea gas equation

PV = nRT

Differentiating both sides with respect to at T at constant pressure.

### Equation of Adiabatic Process

From the first law of thermodynamics

dQ = du + pdv — (i)

For adiabatic process

dQ = 0 (∴ heat constant)

du + Pdv = 0 — (ii)

If Cv is the molar heat capacity at a constant volume for one mole of gas,

du = 1Cvdt — (iii)

using equation (iii) in equation (ii)

CvdT + Pdv = 0 — (iv)

Also ideal gas equation for 1 mole of gas

PV = RT

Differentiating both sides with respect to ‘T’

P dv / dT + V dP / dT = R dT / dT

P dv + vdP = R dT

dT = Pdv + Vdp / R — (v)

using equation (v) in equation (iv)

Cv ( Pdv + Vdp / R ) + Pdv = 0

Cv (Pdv + Vdp) + RPdv = 0

(CV+R) Pdv + CvVdp = 0 [ ∴ cp-cv=R]

CpPdv + CvVdp = 0

Dividing both side by CvPv

Integrating on both sides

**In terms of pressure and volume **

### In terms of temperature and volume

We have,

### In terms of pressure and temperature

**Work done by an isothermal process **

dw = PdV — (i)

Thus total work done

for 1 mole of the gas ideal gas equation be,

PV = RT

P = RT / V — (iii)

using equation (iii) in equation (ii)

### Work done by Adiabatic process

For one mole of gas

Equations (iv) and (iii) are required expressions for n mole of gas during the adiabatic Process.

### Reversible and Irreversible Process

**Fig: PV diagram for a reversible process**

**Fig: PV diagram for an irreversible process**

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