## Tuesday, October 23, 2007

### Study guide H C Verma JEE Physics Ch. 26 LAWS OF THERMODYNAMICS

JEE syllabus :
Equivalence of heat and work;

First law of thermodynamics and its applications (only for ideal gases) 26.1;
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Chapter sections

26.1 The first law of thermodynamics
26.2 Work done by a gas
26.3 Heat engines
26.4 The second law of thermodynamics
26.5 Reversible and irrerversible processes
26.6 entropy
27.7 Carnot engine
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Study plan

Day 1
26.1 The first law of thermodynamics
26.2 Work done by a gas

Day 2
26.3 Heat engines

Day 3
26.4 The second law of thermodynamics
26.5 Reversible and irrerversible processes

Day 4
26.6 entropy
27.7 Carnot engine

Day 5
Worked out examples 1 to 11

Day 6
Exercises 1 to 10

day 7
Exercises 11 to 20

Day 8
Exercises 21 to 22
Objective I

Day 9
Objective II
Questions for short answer 1 to 8

Day 10
Questions for short answer 9 to 15

Revision
Day 11
Concept review

Day 12
Formula revision

Days 13 to 20
Problems from test paper books

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Concepts covered

26.1 We already studied that heat is a form of energy. A system can be given energy either by supplying heat to it or by doing mechanical work on it.

Suppose in a process, an amount of ΔQ of heat is given to the gas and an amount ΔW of work is done by it.

Total energy of the gas must increase by ΔQ - ΔW. If the container along with the gas does not move (you can say that there is no systematic movement) this net energy must go into the system in the form of its internal energy.

If we denote the change in internal energy by ΔU, we can write

ΔU = ΔQ - ΔW or

ΔQ = ΔU + ΔW

The above equation is a mathematical statement of the first law of thermodynamics. The equation represents a statement of conservation of energy and is applicable to any system, however complicated.

The first law may be taken as a statement that there exists an internal energy function U that has a fixed value in a given state. Remember that internal energy is a state function.

Notation for ΔQ and ΔW

If work is done by the system, ΔW is positive. If work is done on the system ΔW is negative.

When heat is given to the system ΔQ is positive. If heat is given by the system to the surroundings ΔQ is negative.

Internal energy increases when heat is given to the system and work is done on the system.

26.2 Work done by a gas

In a cylindrical piston, if the gas expands by a small distance Δx, change in volume is ΔV which is equal to AΔx, where A is cross sectional area of cylinder or piston. As force is equal to pA work done is equal to

ΔW = p*A*Δx = p*ΔV = pΔV

Work done in expansion of from initial volume of V1 to V2 can be found by integrating pΔV and finding its definite integral value between V1 to V2.

ΔW =∫pΔV

This formual even though derived with cylindrical shape, is applicable to any shape.

Expressions for work done in various specified processes

Work done in an Isothermal process:

In an isothermal process Temperature is constant. Hence pV is constant.
For an ideal gas pV = nRT, therefore p = nRT/V

W is given by the expression nRTln[V2/V1]

Work done in an Isobaric Process

IN this process pressure is constant.
Hence W = p(V2-V1)

Work done in an Isocharic Process

As there is no change in volume of gas in this process, work done is zero.

26.5 Reversible and irrereversible processes

If the gas in thermal equilibrium all the parts of gas will be at the same temperature and the state of the gas can described by specifying its pressure, volume and temperature. If we put the container of gas on a hot stove, various parts of the gas will be at different temperatures and we cannot specify a unique temperature for the gas. The gas in not in thermodynamic equilibrium in this case.

If the process is performed in such a way that at any instant during the process the system is very nearly in thermodynamic equilibrium, the process is called quasi-static. Thus, a quasi static process is an idealized process in which all changes take place infinitely slowly. Such a process may be assumed to be reversible.

But a process can be reversible only if it satisfies two conditions. The process must be quasistatic and it should be nondissipative. This means, friction, viscosity etc. should be completely absent.

Reversible cycle: If all parts of cyclic process are reversible, it is called a reversible process.

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Audiovisual lecture

Laws of thermodynamics
www.curriki.org/nroc/Introductory_Physics_1/lesson29/Container.html