- Consider a cylinder filled with gas and equipped with a movable piston as shown in fig below

fig - Force exerted by a system during small expansion.

Suppose,

A - Cross Sectional area of cylinder

P - Pressure exerted by piston at the piston face.

PA - Force exerted by the system.

- If piston moves out by a distance dx then Work done by this force is dW given by

dW = PAdx

= PdV (1)

since V = Adx and dV is change in volume of the system.

- In a finite volume change from V
_{1}to V_{2}

W=∫PdV (2)

where limits of integration goes from V_{1}to V_{2}

Graphically this relationship is shown below

- Thus eqn (2) can be interpreted graphically as area under the curve between limits V
_{1}and V_{2}.

- If pressure remains constant while the volume changes, then work is

W = P(V_{2}-V_{1}) (3)

- Work done not only depends on initial and final states but also on the intermediate states i.e., on the path.

A ideal monatomic gas is taken through the process ABCDA as shown in below P-V diagram. Calculate the Work done by gas

Work done by the gas from A to B = 0 ( as volume constant and area enclosed by AB is zero)

Work done by the gas from B to C = 2PV ( Area enclosed by line BC)

Work done by the gas from C to D = 0 ( as volume constant and area enclosed by AB is zero)

Work done by the gas from D to A = -PV ( Area enclosed by line BC and negative as volume is decreased)

Net Work Done = 2PV - PV = PV

An ideal gas undergoes cyclic process ABCDA as shown in given P-V diagram .The amount of work done by the gas is

Work done by the gas from A to B = 2PV ( Area enclosed by line AB)

Work done by the gas from B to C = 0 ( as volume constant and area enclosed by BC is zero)

Work done by the gas from C to D = -4PV ( Area enclosed by line CD and negative as volume is decreased)

Work done by the gas from D to A = 0 ( as volume constant and area enclosed by DA is zero)

Net Work Done = 2PV - 4PV = -2PV

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

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

Class 11 Maths Class 11 Physics Class 11 Chemistry

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