- We have defined specific heat capacity and molar specific heat capacity earlier in the previous chapter.

- There are two specific heats of ideal gases.

(i) Specific heat capacity at constant volume

(ii) Specific heat capacity at constant pressure

C_{p}and C_{v}are molar specific heat capacities of ideal gas at constant pressure and volume respectively for C_{p}and C_{v}of ideal gas there is a simple relation.

$C_p-C_v = R$ ---(1)

where R- universal gas constant

- This relation can be proved as follows from first law of thermodynamics for 1 mole of gas we have

$ \Delta Q =\Delta U+P \Delta V $ --(2)

- If heat is absorbed at constant volume for the temperature difference $\Delta T$ then ΔV = 0 and

C_{V}=(ΔQ/ΔT)_{V}=(ΔU/ΔT)_{V}-----(3)

If Q in absorbed at constant pressure for the temperature difference $\Delta T$,then

C_{P}=(ΔQ/ΔT)_{P}=(ΔU/ΔT)_{P}+P(ΔV/ΔT)_{P}---- (4)

Now ideal gas equation for 1 mole of gas is

PV = RT

P(ΔV/ΔT) = R --(5)

From (3) and (4)

C_{P}- C_{V}=(ΔU/ΔT)_{P}-(ΔU/ΔT)_{V}+P(ΔV/ΔT)_{P}

Now from equation (5)

C_{P}- C_{V}=(ΔU/ΔT)_{P}-(ΔU/ΔT)_{V}+ R

- Since internal energy U of ideal gas depends only on temperature so subscripts P and V have no meaning.

$C_P - C_V = R$

which is the desired relation

C

or

$\Delta U = C_v \Delta T$

or

$dU= C_v dT$

for n moles for gas

$dU= nC_v dT$

If we take the internal energy at T=0,then

$U=nC_v T$

- Introduction
- Concept of Heat
- P-V Indicator Digram
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- Work done by Gas in volume changes
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- Internal Energy
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- First Law of Thermodynamics
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- Specific Heat Capacity of Ideal GAS
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- Thermodynamic Processes
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- Quasi static Processes
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- Isothermal Process
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- Adiabatic Process
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- Isochoric process
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- Isobaric process
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- Cyclic process
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- Work done in Isothermal process
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- Work done in an Adiabatic process
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- Heat Engine and efficiency
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- Principle of a Refrigerator
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- Second law of thermodynamics
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- Reversibility and irreversibility
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- Carnot's Heat Engine
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- Carnot Theorem
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- Solved Examples

- Thermodynamics Questions
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- Multiple Choice Questions
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- P-V diagram Problems and Solutions
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- Carnot Cycle Problems

Class 11 Maths Class 11 Physics Class 11 Chemistry

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