Calculate ΔE and determine whether the process is endothermic or exothermic for the following cases: (a) q = 0.763 kJ and w = -840 J.

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Convert the work (w) from joules to kilojoules to match the units of heat (q). Since 1 kJ = 1000 J, divide the work value by 1000: \( w = \frac{-840 \text{ J}}{1000} \text{ kJ} \).

Use the first law of thermodynamics, which states that the change in internal energy (\( \Delta E \)) is the sum of heat (q) and work (w): \( \Delta E = q + w \).

Substitute the given values into the equation: \( \Delta E = 0.763 \text{ kJ} + w \text{ (in kJ)} \).

Determine the sign of \( \Delta E \). If \( \Delta E \) is positive, the process is endothermic (absorbs energy). If \( \Delta E \) is negative, the process is exothermic (releases energy).

Interpret the result to conclude whether the process is endothermic or exothermic based on the sign of \( \Delta E \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

First Law of Thermodynamics

The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another. In a closed system, the change in internal energy (ΔE) is equal to the heat added to the system (q) minus the work done by the system (w). This principle is fundamental for understanding energy transfers in chemical processes.

Internal Energy Change (ΔE)

The change in internal energy (ΔE) of a system is calculated using the equation ΔE = q + w, where q represents heat transfer and w represents work done. A positive ΔE indicates that the system has gained energy, while a negative ΔE indicates a loss of energy. This concept is crucial for determining the nature of the process as either endothermic or exothermic.

Endothermic vs. Exothermic Processes

Endothermic processes absorb heat from the surroundings, resulting in a positive q value, while exothermic processes release heat, leading to a negative q value. The sign of ΔE helps classify the process: if ΔE is positive, the process is endothermic; if negative, it is exothermic. Understanding these distinctions is essential for predicting the thermal behavior of chemical reactions.

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Endothermic & Exothermic Reactions Example 2

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(b) What is meant by the internal energy of a system?

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Calculate ΔE and determine whether the process is endothermic or exothermic for the following cases: (b) A system releases 66.1 kJ of heat to its surroundings while the surroundings do 44.0 kJ of work on the system.

Textbook Question

For the following processes, calculate the change in internal energy of the system and determine whether the process is endothermic or exothermic: (a) A balloon is cooled by removing 0.655 kJ of heat. It shrinks on cooling, and the atmosphere does 382 J of work on the balloon. (b) A 100.0-g bar of gold is heated from 25 °C to 50 °C during which it absorbs 322 J of heat. Assume the volume of the gold bar remains constant.

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Textbook Question

A gas is confined to a cylinder fitted with a piston and an electrical heater, as shown here:

Suppose that current is supplied to the heater so that 100 J of energy is added. Consider two different situations. In case (1) the piston is allowed to move as the energy is added. In case (2) the piston is fixed so that it cannot move. (a) In which case does the gas have the higher temperature after addition of the electrical energy?