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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Identify the given values: the heat removed from the system \( q = -0.655 \text{ kJ} \) and the work done on the system \( w = 382 \text{ J} \).

Convert all units to the same system for consistency. Since \( q \) is in kJ, convert \( w \) from J to kJ: \( w = 0.382 \text{ kJ} \).

Use the first law of thermodynamics, which states \( \Delta U = q + w \), where \( \Delta U \) is the change in internal energy.

Substitute the values into the equation: \( \Delta U = -0.655 \text{ kJ} + 0.382 \text{ kJ} \).

Determine if the process is endothermic or exothermic: if \( \Delta U \) is negative, the process is exothermic; if positive, it is endothermic.

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Key Concepts

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

Internal Energy

Internal energy is the total energy contained within a system, encompassing both kinetic and potential energy of the particles. It is a state function, meaning it depends only on the current state of the system, not on how it reached that state. Changes in internal energy can be calculated using the first law of thermodynamics, which states that the change in internal energy equals the heat added to the system minus the work done by the system.

Endothermic and Exothermic Processes

Endothermic processes absorb heat from the surroundings, resulting in a decrease in the temperature of the surroundings, while exothermic processes release heat, increasing the temperature of the surroundings. The classification of a process as endothermic or exothermic is determined by the sign of the heat transfer: positive for endothermic (heat absorbed) and negative for exothermic (heat released). Understanding these concepts is crucial for analyzing energy changes in chemical and physical processes.

Work Done on/by the System

In thermodynamics, work is defined as the energy transfer that occurs when a force is applied over a distance. When work is done on the system, it is considered positive, as it adds energy to the system. Conversely, when the system does work on the surroundings, it is negative. This distinction is important for calculating the overall change in internal energy, as it directly influences the energy balance in the system.

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Textbook Question

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

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?

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. (b) Identify the sign (positive, negative, or zero) of q and w in each case?

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Textbook Question

Consider a system consisting of two oppositely charged spheres hanging by strings and separated by a distance r1, as shown in the accompanying illustration. Suppose they are separated to a larger distance r2, by moving them apart. (a) What change, if any, has occurred in the potential energy of the system?