First Law of Thermodynamics : Work Done In Different Thermodynamic Processes

Isobaric Processes:

• Concepts:

  • Work done during isobaric expansion is positive, while work done during isobaric compression is negative.
  • The work done is equal to the product of pressure and the change in volume.

• Formula: $$W = -P\Delta V$$

• Reference: NCERT Physics Class 12, Chapter 13, Section 13.5.1

Isochoric Processes:

• Concepts:

  • No work is done during an isochoric process, as the volume remains constant.

• Formula: $$W = 0$$

• Reference: NCERT Physics Class 12, Chapter 13, Section 13.5.1

Isothermal Processes:

• Concepts:

  • Work done during an isothermal expansion is negative, while work done during an isothermal compression is positive.
  • The work done is equal to the product of the pressure and the natural logarithm of the change in volume.

• Formula: $$W = -nRT\ln\frac{V_f}{V_i}$$

• Reference: NCERT Physics Class 12, Chapter 13, Section 13.5.2

Adiabatic Processes:

• Concepts:

  • No heat is transferred during an adiabatic process.
  • The work done is equal to the negative change in internal energy.

• Formula: $$W = -\Delta U$$

• Reference: NCERT Physics Class 12, Chapter 13, Section 13.5.3

Reversible and Irreversible Processes:

• Concepts:

  • A reversible process is one that can be reversed without leaving any changes in the system or the surroundings.
  • An irreversible process is one that cannot be reversed without leaving some changes in the system or the surroundings.

• Reference: NCERT Physics Class 12, Chapter 13, Section 13.6

Cyclic Processes:

• Concepts:

  • A cyclic process is one in which the system returns to its initial state after undergoing a series of changes.
  • The work done in a cyclic process is equal to the net heat added to the system.

• Formula: $$W = \oint PdV$$

• Reference: NCERT Physics Class 12, Chapter 13, Section 13.7

Efficiency of Heat Engines:

• Concepts:

  • Efficiency of a heat engine is defined as the ratio of the work done by the engine to the heat input.
  • Carnot’s theorem states that the most efficient heat engine is a reversible engine operating between the same two temperatures.

• Formula: $$\eta = \frac{W_{net}}{Q_H}$$

• Reference: NCERT Physics Class 12, Chapter 13, Section 13.8