Internal energy(ΔE) is equal to the heat supplied(q) ina)Adiabatic changeb)Isochoric changec)Isothermal reversible changed)Isothermal irreversible changeCorrect answer is option 'B'. Can you explain this answer?

Question

Internal energy(&Delta;E) is equal to the heat supplied(q) ina)Adiabatic changeb)Isochoric changec)Isothermal reversible changed)Isothermal irreversible changeCorrect answer is option 'B'. Can you explain this answer?

Answer

Internal Energy and Heat in Different Processes:

Internal energy (ΔE) is a property of a system that represents the sum of all microscopic forms of energy in the system. Heat supplied (q) is the transfer of thermal energy between systems at different temperatures. The relationship between internal energy and heat supplied varies depending on the process.

Internal energy (ΔE) is equal to the heat supplied (q) in an isochoric change:
- In an isochoric change, the volume of the system remains constant.
- Since there is no change in volume, no work is done by the system.
- Therefore, any heat supplied to the system is used to increase the internal energy of the system.
- The change in internal energy (ΔE) is directly proportional to the heat supplied (q) in an isochoric process.

In other processes:
- Adiabatic change: In an adiabatic change, no heat is exchanged between the system and its surroundings. Therefore, the change in internal energy is solely due to work done on or by the system.
- Isothermal reversible change: In an isothermal reversible change, the temperature of the system remains constant. Any heat supplied is used to do work rather than increase internal energy.
- Isothermal irreversible change: In an isothermal irreversible change, there is energy dissipation due to irreversibilities, so the heat supplied does not solely increase the internal energy of the system.

Therefore, in an isochoric change, where the volume remains constant, internal energy is equal to the heat supplied.

Answer

For Isochoric change, ΔV = 0 w = PΔV = 0 S
ince, ΔE = q + w
This implies, ΔE = q

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