Thermodynamics:

The branch of physics mainly concerned with the transformation of heat into mechanical work and vice–versa is called thermodynamics.

Thermodynamic System:
Types of thermodynamic system

A definite quantity of matter (atoms or molecules) enclosed by a boundary surface is called a system. Anything outside the system is called surrounding. A thermodynamic system may exchange energy and matter with the surroundings.

(1) Open system: Which can exchange energy and matter with the surroundings e.g. water boiling in a vessel, open vessel.

(2) Closed system A system which can exchange only energy with surrounding is called closed system e.g closed hot pot.

(3) Isolated system : A system which can’t exchange anything with the surrounding is called Isolated system e.g. Closed vessel with insulated walls, Thurmas.

Thermodynamic Parameter:

The parameters which are used to specify the state of thermodynamic system. e.g. Pressure, volume, Temperature entropy internal energy e.t.c.

Work done by gas during Expansion:

If a system undergoes a displacement under the action of a force work is said to be done.

Consider a system of gas in a cylinder provided with frictionless and movable piston of cross-sectional area A. At any instant Let P, V and T be the state of gas.

When the gas is expanded suppose the piston is displaced by a small distance ‘dx’. Small work done by the gas is given by

𝒅𝑾 = 𝑭 𝒅𝒙 = 𝑷𝑨 𝒅𝒙 = 𝑷 𝒅𝑽 (∵ 𝑨 𝒅𝒙 = 𝒅𝑽)

For total work done,𝑾 = 𝒅𝑾 = 𝑽𝟏 𝑽𝟐 𝑷 𝒅𝑽 → (𝟏)

∴ 𝑾 = 𝑷 (𝑽𝟐 − 𝑽𝟏)

• Case (i): for expansion, 𝑽𝟐 > 𝑽𝟏 ⇒ 𝑾 = +𝒗𝒆, work done by gas

• Case (ii): for compression, 𝑽𝟐 < 𝑽𝟏 ⇒ 𝑾 = −𝒗𝒆, 𝒘𝒐𝒓𝒌 𝒅𝒐𝒏𝒆 𝒐𝒏 𝒈𝒂s

Sign convention for a thermodynamic process:

- If work is done on the system w = +ve

If work is done on the system w = -ve

- For the expansion of gas w = +ve

For the compression of gas w = -ve

- Heat gained (added )by a system is +ve

Heat lost (extracted) by a system is –ve

- Increase in internal energy of a system is taken as +ve and decrease in internal energy of a system is then -ve .

Indicator diagram (p-v diagram)

The pressure in equation (1) above may vary during the change in volume. In such cases the work done is determined by PV diagram.

Suppose a gas expands from initial state A (𝑷𝟏, 𝑽𝟏) to the final state B (𝑷𝟐, 𝑽𝟐) as shown in fig. Let E be a point and P and V be the pressure and volume at that point. Let the volume increases by small amount dV at const. pressure to a point F which is close to E.

Now,

Work done during a small change of volume dV.

dw = P dV = Area of EFGH

∴ Total work done by the gas from A (𝑷𝟏, 𝑽𝟏) to B (𝑷𝟐, 𝑽𝟐) = Area of ABCD.

Work done by a system is numerically equal to area under P- V diagram.

Work done by a gas in cyclic process

When a system passing through different states returns to it’s initial state then it is called cyclic process.

Consider a thermodynamic system initially at state A (𝑷𝟏, 𝑽𝟏) . When the gas is expanded suppose the system reaches to state B (𝑷𝟐, 𝑽𝟐) along path AEB as shown in fig.

Work done during expansion

𝑊1= Area of AEBCDA

Further when the gas is compressed suppose the system reaches to it’s initial state A (𝑷𝟏, 𝑽𝟏) from B (𝑷𝟐, 𝑽𝟐) along the path BFA .

Work done during compression

𝑊2= Area of BFADCB

Therefore, Net work done in cyclic process

W = 𝑊1+(-𝑊2)

= Area of AEBFA

Therefore, Area enclosed by the cyclic curve gives the work done during Cyclic process.

Internal Energy (u)

The sum of kinetic energy and potential energy of any system or (for all molecules of gas ) is called internal energy.
The molecules of gas are in random motion so they possess K.E .So it is function of temperature.
The molecules also have their intermolecular forces of attraction which possess the P.E.
A real gas possess both type of internal energy so ‘u’ is the function of T and V but in an ideal gas there is absence of intermolecular force that means no pot. Energy so internal energy is function of temp.
Note : For cycle process du = o

First Law of thermodynamics:

It states that the amount of heat supplied to a system (dQ) is equal to the sum of the increase in internal energy (dU) of the system and the external work done by the system (dW)

ie. dQ = dU + dW

Since we have, dw = P dV

dQ = du + P dV

(Simply conservation of Energy )

Note : dQ is taken +ve if heat is given to the system and – ve if heat is taken off from the system.

Heat Capacities of gas

Gas can be heated by keeping pressure constant and by keeping volume constant and Since, different amount of heat is required when the gas is heated at constant pressure and at constant volume for the same change in temperature, therefore the gas have two different values of heat capacities.

The heat capacity defined in terms of standard mass system (in one Kg or one gram) is called principle specific heat or specific heat capacity. The heat capacity defined in terms of molar mass (in one mole) is called as molar specific heat or molar heat capacity.

Thermodynamical process:

A process by which one or more parameters of thermodynamic system undergo a change is called as thermodynamic process or a thermodynamical change.

The various types of thermodynamical processes are:

(a) Isothermal process

(b) Adiabatic process

(d) Isochoric process

LIMITATIONS OF FIRST LAW OF THERMODYNAMICS.

1. I law of thermodynamics explains the conversion of heat energy into mechanical work but cannot explain the extent of conversion.

2. This law explains the flow of heat from hot body to cold body but cannot explain why heat cannot flow from cold body to hot body.

3. It could not explain the efficiency of heat engine.

Second Law of Thermodynamics:

1.Heat Engine:

A heat engine is a device that converts the heat energy into mechanical energy and some external work is done.

2.Types of heat Engine :

i) Internal Combustion heat Engine

Fuel burns inside e.g. Diesel engine, petrol engine etc.

ii) External Combustion heat Engine

Fuel burns outside the engine e.g steam engine.

3.Major parts of heat engine:

i) Source : A source is a hot body at a constant high temperature from which any amount of heat can be drawn without changing it’s temperature.

ii) Sink: Sink is a cold body at a constant low temperature to which any amount of heat can be rejected without changing it’s temperature.

iii) Working Substance : A substance which absorbs the heat energy from the source , converts a part of heat energy into mechanical work and rejects the remaining heat energy to the sink.

e.g. steam in steam engine, mixture of air and fuel in internal combustion engine.

4.Efficiency of Heat engine:

5.Second Law of Thermodynamics:

a) Kelvin’s Statement: “ It is impossible to get a continuous supply of work from a body by cooling it to a temperature lower than that of it’s surrounding.”

It clears about, sink is necessary and heat engine can not work if the temperature of source is equal to temperature of sink.

b) Clausius Statement : “It is impossible to make heat flow from a body at a lower temperature to a body at a higher temperature without doing external work on the working substance.”

Or “ It is impossible to design a self acting machine unaided by any external agency , which would transfer heat from a body at a lower temperature to another body at a higher temperature.”

6.Carnot Engine ( Ideal heat engine ):

Carnot engine is an ideal reversible heat engine which is free from all the defects of practical engine. It is never possible to realize this engine in practice. It consists of four parts which are

i) Source: The source of infinite thermal heat capacity having three non conducting and one conducting wall which is maintained at a fixed high temperature 𝑇1 from which heat engine can draw heat.

ii) Sink : The sink remains at constant lower temperature 𝑇2 to which any amount of heat can be rejected , having three non conducting and one conducting wall.

iii) Working Substance : A cylinder with perfectly insulating walls and conducting base fitted with a frictionless and air tight insulating piston consist ideal gas as the working substance.

iv) Stand: On operating the working substance , the insulated stand is used to place the working substance on it.

Carnot cycle : Consider n mole of gas enclosed in the cylinder. Let the initial state of the gas is A(𝑃1, 𝑉1, 𝑇1)

Isothermal Expansion :

Place the engine containing working substance over the source at temperature 𝑇1 and allow to expand . In this process the system changes it’s state from A(𝑃1, 𝑉1) to B(𝑃2, 𝑉2 ) at constant temperature 𝑇1 by absorbing 𝑄1 amount of heat from the source.

Work done during this process

𝑊1 = 𝑄1 = n R 𝑇1 ln (𝑉2 𝑉1 ) = Area of ABGEA → (𝑖)

Adiabatic Expansion:

Place the engine on the stand having an insulated top. Volume increases adiabatically till the temperature up to sink . In this process the system changes it’s state from B(𝑃2, 𝑉2) at temp. 𝑇1 to C(𝑃3, 𝑉3 ) at temp. 𝑇2

Work done during this process

𝑊2 = n r 𝛾−1 (𝑇1- 𝑇2) = Area of BCHGB → (𝑖𝑖)

Now net work done in one complete cycle

W = 𝑊1 + 𝑊2+ 𝑊3 + 𝑊4

= n R 𝑇1 ln (𝑉2/ 𝑉1 ) - n R 𝑇2 ln (𝑉3/ 𝑉4 )

= Area of ABCDA = Area of carnot cycle . → (𝑣)

Note:

i) Efficiency depends on temp. of source 𝑇1 and sink 𝑇2 ,

ii) In equation , RHS < 1 ∴ Ƞ< 100%

iii) For Ƞ = 1 either 𝑇1 = ∞ or 𝑇2= 0K which are not attainable.

iv) If 𝑇1 = 𝑇2 then Ƞ = 0 ( not possible to convert heat to work )

7.Petrol Engine :

Petrol engine is designed by otto in 1876 and hence it is also called otto engine .It is internal combustion engine in which a mixture of air and petrol ( 98% 𝑎𝑖𝑟 𝑎𝑛𝑑 2% 𝑝𝑒𝑡𝑟𝑜𝑙 ) is used as working substance.

Construction:

It consists of a cylinder fitted with the piston. The cylinder is provided with inlet valve ‘I’ and outlet valve ‘O’ . A spark plug is also placed in the cylinder.

Working :

The working of petrol engine is divided into four steps as shown in fig.

i) Suction stroke :

Inlet valve I is open , piston is moved downward and exhaust valve O is closed .It sucks 98% 𝑎𝑖𝑟 𝑎𝑛𝑑 2% 𝑝𝑒𝑡𝑟𝑜𝑙 at atmospheric pressure . This process is represented by AB on PV-diagram.

ii) Compression Stroke :

In this stroke both valves are closed by moving the piston inward . The mixture undergoes adiabatic compression and it’s volume is reduced about 1 5 th of the original volume. As a result the temperature of the mixture raised to about 600°c . This process is represented by BC on PV-diagram.

iii ) Ignition and working stroke:

Spark plug S is switched on so mixture of air and petrol burn at constant volume ,represented by CD .So 𝑄1 amount of heat is generated and temp. becomes about 2000°c and pressure 15 atm.

In working stroke the mixture is completely burned and it pushes the piston downward and expansion occurs adiabatically and work is done which is represented by DE.

iv) Exhaust stroke :

Outlet valve O is open ,smoke come out ,pressure decreases and 𝑄2 amount of heat is rejected at constant volume, shown by EB in P-V diagram.

Finally the burnt gases are forced out from the cylinder with the inward movement of piston and volume decreases which is shown by BA.

# Merits and Demerits of a Petrol Engine:

Merits of Petrol Engine	Demerits of Petrol Engine
1. High power output	1. Lower fuel efficiency
2. Smooth and quiet operation	2. Higher operating costs
3. Quick acceleration	3. Higher emissions
4. Widespread availability	4. Flammable
5. Lower initial cost	5. Less torque
6. Lighter weight	6. Maintenance costs
7. Lower emissions	7. Noise pollution

8. Diesel Engine :

Diesel engine was designed by Rudolf Diesel in 1892 .It is an internal combustion engine in which air is working substance and diesel is fuel.

Construction:

It consists of a cylinder provided with three valves namely air inlet valve I , oil supply valve O and exhaust valve E.

Working :

The working of diesel engine is divided into four steps:

Fig: Four Stokes of a diesel engine. Fig. P-V diagram of the diesel engine.

Suction stroke :

Air valve I is opened and pure air at atmospheric pressure is drawn into the cylinder by the outward motion of the piston which is represented by AB on the P-V diagram.

Compression stroke:

All valves are closed and air is compressed adiabatically to about 1/16 th of it’s initial volume by the backward motion of the piston , air pressure inside the cylinder becomes 34 atmospheres and temp. equal to about 1000°c , represented by BC on P-V diagram.

Working stroke:

The oil valve O is opened and the diesel oil is sprayed into the hot air inside cylinder. Due to high temp. inside, the oil burns spontaneously and 𝑄1 amount of heat is supplied to gas .The gas expands at constant pressure along the line CD. When temp. reaches about 2000K the supply of oil is cut off ( at D ) .The hot air expands adiabatically and the piston moves in the outward direction in which useful work is done, represented by DE.

Exhaust stroke :

The exhaust valve E opens ( at E ) and the burnt out gases are driven out until the pressure falls to the atmospheric pressure i.e. 𝑄2 amount of heat is rejected at constant volume so that the temperature and pressure decrease which is represented by EB .Now from position B , the piston moves inside and the rest of combustion products are exhausted at constant pressure , represented by BA.

Merits and Demerits of a Diesel Engine:

Merits of Diesel Engine	Demerits of Diesel Engine
1. Excellent Mileage	1. Expensive
2. No Tune-up required	2. Low Energy Content of Diesel Fuel
3. More Durable than Gasoline Engines	3. Diesel Fuel more Expensive
4. Higher Torque	4. Lags in acceleration
5. Higher Strength	5. High Maintenance
6. Good lubrication properties

Note: The compression ratio in a diesel engine is very high . Due to high compression ratio the temp. achieved are sufficient to ignite the fuel mixture without use of spark plug.

Easy Notes Nepal

Thermodynamics 12| Heat and Thermodynamics |Physics Note