Calculate ΔE, and determine whether the process is...

Calculate $\Delta E$, and determine whether the process is endothermic or exothermic for the following cases: (a) A system absorbs $105 \mathrm{~kJ}$ of heat from its surroundings while doing $29 \mathrm{~kJ}$ of work on the surroundings; (b) $q=1.50 \mathrm{~kJ}$ and $w=-657 \mathrm{~J} ;$ (c) the system releases $57.5 \mathrm{~kJ}$ of heat while doing $22.5 \mathrm{~kJ}$ of work on the surroundings.

Key Concepts

First Law of Thermodynamics

This principle states that the change in the internal energy of a system (?E) is equal to the sum of the heat exchanged (q) and the work done (w) by or on the system. It is the foundation of energy conservation in thermodynamic processes.

Internal Energy (?E) Calculation

The internal energy change (?E) of a system is calculated using the equation ?E = q + w, where q represents the heat transfer and w represents the work done. This calculation helps determine how energy is added to or removed from a system during a process.

Heat Transfer and Process Type

Understanding whether a process is endothermic or exothermic relies on the sign of the heat transfer. Heat absorbed by the system (q positive) indicates an endothermic process, while heat released from the system (q negative) indicates an exothermic process.

Sign Conventions for Work

In thermodynamic calculations, the sign of work is crucial. Work done by the system on its surroundings is typically taken as negative, whereas work done on the system is positive. This sign convention ensures that the energy change of the system is accounted for correctly.

Unit Conversion

Accurate calculations often require unit consistency. When work and heat are provided in different units (e.g., kilojoules and joules), converting all values to the same unit is essential to correctly perform the calculation of ?E.

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