There are other forms of work besides P-V work. For example,...

There are other forms of work besides $P-V$ work. For example, electrical work is defined as the potential $\times$ change in charge, $w=\phi \Delta q .$ If a charge in a system is changed from $10 \mathrm{C}$ to $5 \mathrm{C}$ in a potential of $100 \mathrm{V}$ and $45 \mathrm{J}$ of heat is liberated, what is the change in the internal energy? (Note: $1 \mathrm{V}=1 \mathrm{J} / \mathrm{C})$

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Key Concepts

Sign Conventions in Thermodynamics

Understanding sign conventions is essential when dealing with energy calculations. Typically, heat added to the system and work done by the system are taken as positive, whereas heat lost by the system and work done on the system are considered negative. This helps in consistently applying the first law of thermodynamics.

Internal Energy

Internal energy refers to the total energy contained within a system, encompassing both kinetic and potential energies at the molecular level. Changes in internal energy result from the net effects of heat transfer into or out of the system and work done by or on the system.

First Law of Thermodynamics

The first law of thermodynamics states that the change in a system's internal energy is equal to the heat added to the system minus the work done by the system. This principle is fundamental for analyzing energy exchanges in any process where work and heat are involved.

Electrical Work

Electrical work is a specific form of work that involves the transfer of electrical energy. It is defined as the product of an electric potential (voltage) and the change in electrical charge, analogous to how mechanical work is the product of force and displacement.

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