A system undergoes a process consisting of the following two...

A system undergoes a process consisting of the following two steps: Step 1: The system absorbs $72 \mathrm{~J}$ of heat while $35 \mathrm{~J}$ of work is done on it. Step 2: The system absorbs $35 \mathrm{~J}$ of heat while performing $72 \mathrm{~J}$ of work. Calculate $\Delta E$ for the overall process.

A system undergoes a process consisting of the following two steps:

Step 1: The system absorbs $72 \mathrm{~J}$ of heat while $35 \mathrm{~J}$ of work is done on it.

Step 2: The system absorbs $35 \mathrm{~J}$ of heat while performing $72 \mathrm{~J}$ of work.
Calculate $\Delta E$ for the overall process.

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Key Concepts

Sign Conventions in Thermodynamics

Understanding sign conventions is crucial when applying the first law. Typically, heat added to the system is considered positive. Work is a bit trickier: when work is done by the system, it is often taken as positive in one version of the convention (leading to ?E = Q - W), whereas when work is done on the system, it is considered positive in the alternate convention (leading to ?E = Q + W). Consistency in the chosen sign convention is essential for correct calculations of energy changes.

Internal Energy Change

This concept refers to the net change in the system's total energy as a result of heat transfer and work interactions. It is the key quantity calculated using the first law of thermodynamics and reflects how energy is stored within the system after all the interactions have taken place.

First Law of Thermodynamics

This principle states that the change in the internal energy of a system is equal to the net heat added to the system plus the net work done on the system. It provides a framework for tracking energy transfers in a process, ensuring energy conservation even when heat and work are exchanged in different directions.

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