Question

A gas absorbs 45 kJ of heat and does 29 kJ of work. Calculate \(\Delta E .\)

Short answer

The change in internal energy of the gas is \(\Delta E = 74 \,\text{kJ}\).

Step-by-step solution

Identify the given values and the formula for the First Law of Thermodynamics

We are given: - \(q = 45 \,\text{kJ}\) (heat absorbed by the gas) - \(w = 29 \,\text{kJ}\) (work done by the gas) We will use the formula for the first law of thermodynamics: \[\Delta E = q + w\]

Substitute the given values into the formula

Now, we substitute the given values into the formula: \[\Delta E = 45 \,\text{kJ} + 29 \,\text{kJ}\]

Solve for the change in internal energy

We now calculate the change in internal energy by adding the two given values: \[\Delta E = 74 \,\text{kJ}\] The change in internal energy of the gas is \(\Delta E = 74 \,\text{kJ}\).

Key concepts

Internal Energy

Internal energy is the total energy contained within a system. It includes all the various types of energy that are stored within the molecules of a substance. Think of it as the energy that is intrinsic to the molecules and atoms, including both kinetic energy (due to their motion) and potential energy (due to their positions).

Role in Thermodynamics

In the context of the First Law of Thermodynamics, internal energy plays a crucial role. This law states that energy cannot be created or destroyed, only transformed or transferred. The change in internal energy (\(\Delta E\) of a system can be calculated by adding the heat exchanged (\(q\)) with the work done (\(w\)) on or by the system:

• If positive, internal energy increases.
• If negative, internal energy decreases.

Recognizing how internal energy affects a system is vital in understanding energy transfer processes.

Heat

Heat is a form of energy transfer that occurs between a system and its surroundings because of a temperature difference. It moves naturally from a hotter to a cooler object until thermal equilibrium is reached, much like water flows from a higher to a lower height.

Heat and the First Law

In thermodynamics, heat plays a central role. It is denoted by \(q\) in the First Law of Thermodynamics, expressing how energy is absorbed or released by a system.

• When a system absorbs heat, \(q\) is positive.
• When a system releases heat, \(q\) is negative.

This transfer can happen in various ways, such as conduction, convection, or radiation. Understanding how heat impacts a system helps in analyzing energy transformations and in maintaining systems in desired states.

Work

Work, in the context of thermodynamics, refers to the transfer of energy by any means other than heat. It often involves a force causing the displacement of an object, like the expansion or compression of gases. When you inflate a balloon, the work done is evident as you pump air into it, causing it to expand.

Thermodynamic Work

Under the First Law of Thermodynamics, work is represented by \(w\). It quantifies how much energy is used to perform a task or power a process, impacting internal energy.

• If the system performs work on its surroundings, \(w\) is negative.
• If work is done on the system, \(w\) is positive.

The way work interacts with other energy forms in a thermodynamic system is essential for evaluating processes like engine operations, refrigeration cycles, and heat pumps.