If du represents the increase in internal energy of a...

If du represents the increase in internal energy of a thermodynamic system and dw the work done by the system, which of the following statement is true? (A) $\mathrm{du}=\mathrm{dw}$ in isothermal process (C) $\mathrm{du}=-\mathrm{dw}$ in an aidabatic process (B) $\mathrm{du}=\mathrm{dw}$ in aidabatic process (D) $\mathrm{du}=-\mathrm{dw}$ in an isothermal process

If du represents the increase in internal energy of a thermodynamic system and dw the work done by the system, which of the following statement is true?
(A) $\mathrm{du}=\mathrm{dw}$ in isothermal process
(C) $\mathrm{du}=-\mathrm{dw}$ in an aidabatic process
(B) $\mathrm{du}=\mathrm{dw}$ in aidabatic process
(D) $\mathrm{du}=-\mathrm{dw}$ in an isothermal process

Key Concepts

First Law of Thermodynamics

This law states that energy is conserved in a thermodynamic process. It relates the change in internal energy of a system (du) to the heat added to the system and the work done by the system. In many formulations, when the work done by the system is considered, the expression is often written as du = dQ - dw, establishing the balance between heat, work, and internal energy changes.

Sign Conventions in Work and Energy

The sign convention for work and energy in thermodynamic systems is essential for correctly applying the first law. When work is defined as the work done by the system (dw), it is treated as energy leaving the system. Consequently, if the system does positive work, its internal energy decreases unless compensated by an equal or greater amount of heat added.

Isothermal Process

An isothermal process is a thermodynamic process in which the temperature of the system remains constant. For ideal gases, this implies that the internal energy, which is a function of temperature, remains unchanged (du = 0). As a result, any work done by or on the system must be exactly balanced by heat exchange with the surroundings to maintain constant internal energy.

Adiabatic Process

An adiabatic process is one in which no heat is exchanged between the system and its surroundings (dQ = 0). Under this condition, the first law of thermodynamics simplifies to du = -dw, indicating that any work done by the system results in a corresponding decrease in its internal energy, or work done on the system results in an increase in its internal energy.

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