## Tuesday, October 23, 2007

### Study guide H C Verma JEE Physics Ch. 27 SPECIFIC HEAT CAPACITIES OF GASES

JEE syllabus

Specific heats (Cv and Cp for monoatomic and diatomic gases)27.1,27.2,27.3,27.4,
Isothermal and adiabatic processes 27.5 27.6, 27.7

27.1 Two kinds of specific heat capacities
27.2 Relation between Cp and Cv for an ideal gas
27.3 Determination of Cp of a Gas
27.4 Determination of Cv of a Gas
27.6 Relations between p,v, t in a reversible adiabatic process
27.7 Work done in a adiabatic process
27.8 Equipartition of energy

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Study Plan

27.1 Two kinds of specific heat capacities
27.2 Relation between Cp and Cv for an ideal gas
27.3 Determination of Cp of a Gas
27.4 Determination of Cv of a Gas
27.6 Relations between p,v, t in a reversible adiabatic process
27.7 Work done in a adiabatic process
27.8 Equipartition of energy

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Concepts covered
Day 1
27.1 Two kinds of specific heat capacities
27.2 Relation between Cp and Cv for an ideal gas

Day 2
27.3 Determination of Cp of a Gas
27.4 Determination of Cv of a Gas

Day 3
Worked out examples 1 to 5

Day 4
27.6 Relations between p,v, t in a reversible adiabatic process

Day 5
27.7 Work done in a adiabatic process
27.8 Equipartition of energy

Day 6
WOE 6 to 12

Day 7
Exercises 1 to 10

Day 8
Exercises 11 to 20

Day 9
exercises 21 to 30

Day 10
Exercises 31 to 35
Objective objective I

Day 11
Obejctive II

Day 12

Day 13
Concept Review

Day 14
Formula Revision

Days 15 to 20
Additional problems from test paper books

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27.1
We already know that specific heat capacity of a substance is defined as the heat supplied per unit mass of the substance per unit rise in the temperature.

In terms of symbols if an amount of ΔQ of heat is given to a mass of n of the substance and its temperature rises by ΔT, the specific heat capacity s is given by the equation

s = ΔQ/mΔT .......(27.1)

This definition is applicable to solids, liquids and gases.

Specific heat capacity of a gas depends on the process involved. Two specific processes are important and specific heat capacities are defined specifically for these processes.

Constant volume process and constant pressure process

When the volume of a gas of mass m is kept constant and heat is given it, the specific heat capacity calculated is called the specific heat capacity at constant volume and is denoted by symbol sv.

When the pressure of a gas of mass m is kept constant and heat is given it, the specific heat capacity calculated is called the specific heat capacity at constant pressure and is denoted by symbol sp.

The molar heat capacities of a gas are defined as the heat given per mole of the gas per unit rise in the temperature.

The molar heat capacity at constant volume is denoted by symbol Cv.

Cv. = ΔQ/nΔT .......(27.4)heat is given at constant volume of the gas
Where n = number of moles gas

The molar specific heat capacity at constant pressure is denoted by symbol Cp.

Cp. = ΔQ/nΔT .......(27.5) heat is given at constant pressure.

Note that quite often, the term specific heat capacity or specific heat is used for molar heat capacity also. To find out the implied meaning you have to note the units given.

The unitof specific heat capacity is J/Kg-K where as that of molar heat capacity is J/mol-K.

27.2