Problem 26 - Chemistry: The Central Science in SI Units, Global Edition

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 \(0.655 \mathrm{~kJ}\) of heat. It shrinks on cooling, and the atmosphere does \(382 \mathrm{~J}\) of work on the balloon. (b) A 100.0-g bar of gold is heated from \(25^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\) during which it absorbs \(322 \mathrm{~J}\) of heat. Assume the volume of the gold bar remains constant.

Step-by-Step Solution

Answer

In summary: (a) The change in internal energy is \(-273 \mathrm{~J}\), and the process is exothermic. (b) The change in internal energy is \(322 \mathrm{~J}\), and the process is endothermic.

Step 1: Determine the heat (q) given to the system

We are given that 0.655 kJ of heat is removed from the system, which means q = -0.655 kJ. We need to convert this into J (joules) for consistency: \(q = -0.655 \times 1000 = -655 \mathrm{~J}\).

Step 2: Determine the work (w) done on the system

We are given that the atmosphere does 382 J of work on the system, which means w = 382 J.

Step 3: Calculate the change in internal energy (ΔU)

We can now use the formula to calculate the change in internal energy (ΔU). ΔU = q + w = (-655 J) + (382 J) = -273 J

Step 4: Determine if the process is endothermic or exothermic

Since the change in internal energy (ΔU) is negative, the process is exothermic. The balloon loses energy to its surroundings as it cools. For case (b)...

Step 1: Determine the heat (q) given to the system

We are given that the gold bar absorbs 322 J of heat, which means q = 322 J.

Step 2: Determine the work (w) done on the system

Since the volume of the gold bar remains constant, there is no work done on the system. Therefore, w = 0 J.

Step 3: Calculate the change in internal energy (ΔU)

We can now use the formula to calculate the change in internal energy (ΔU). ΔU = q + w = (322 J) + (0 J) = 322 J

Step 4: Determine if the process is endothermic or exothermic

Since the change in internal energy (ΔU) is positive, the process is endothermic. The gold bar gains energy from its surroundings as it is heated. To summarize, the process in case (a) is exothermic, and the change in internal energy is -273 J. The process in case (b) is endothermic, and the change in internal energy is 322 J.

Key Concepts

Internal Energy

Internal energy is the total energy contained within a system. It includes all kinds of energy such as kinetic and potential energy of the molecules in the substance. Internal energy is an essential concept in thermodynamics, often represented by the symbol \( U \).

To understand how internal energy works, you need to consider both the heat transferred to or from the system and the work done on or by the system.

• Heat (q): This is the energy exchanged because of temperature differences. A system can absorb or release heat.
• Work (w): This is the energy transferred when a force moves an object. In thermodynamics, we often talk about work done by or on a gas, like when a balloon expands or contracts.

The change in internal energy, denoted as \( \Delta U \), is given by the equation:
\[ \Delta U = q + w \]
In this equation:

• \( q \) is positive if the system absorbs heat and negative if it releases heat.
• \( w \) is positive if work is done on the system and negative if the system does work on its surroundings.

Endothermic Process

An endothermic process is an occurrence in which the system absorbs energy from its surroundings. This is reflected as an increase in its internal energy. Some examples of endothermic processes include melting ice and boiling water, where energy is required to change the phase.

In terms of thermodynamics, for a process to be considered endothermic, the change in internal energy \( \Delta U \) is positive. This means:

• The system gains heat from its surroundings.
• The surroundings effectively cool down because energy is transferred to the system.

In the exercise example with the gold bar, when it absorbed 322 J of heat without performing work, the internal energy increased by 322 J. This demonstrates that the heating of the gold bar is endothermic, as energy is taken from the surroundings to raise its temperature.

Exothermic Process

An exothermic process is one where the system releases energy to its surroundings, causing a decrease in the internal energy of the system. Common examples include burning wood or a car engine running, where energy is output as heat and often light.

In thermodynamics, a process is classified as exothermic when the change in internal energy \( \Delta U \) is negative. This indicates that:

• The system releases heat to its surroundings.
• The surroundings get warmer as they absorb this released energy.

For instance, in the exercise with the shrinking balloon, internal energy changes by -273 J, showing that energy is lost to the surroundings as heat. The cooling balloon, therefore, is undergoing an exothermic process, where energy escapes to the air, reducing its internal energy.