Question

Which statement is true of the internal energy of the system and its surroundings following a process in which \(\Delta E_{\mathrm{sys}}=+65 \mathrm{~kJ} ?\) Explain. a. The system and the surroundings both lose 65 kJ of energy. b. The system and the surroundings both gain 65 kJ of energy. c. The system loses \(65 \mathrm{~kJ}\) of energy and the surroundings gain \(65 \mathrm{~kJ}\) of energy. d. The system gains 65 kJ of energy and the surroundings lose

Short answer

The system gains 65 kJ of energy and the surroundings lose 65 kJ of energy.

Step-by-step solution

Understand the Conservation of Energy

First, recall that the First Law of Thermodynamics indicates energy is conserved in any process. This law can be expressed as \(\Delta E_{\text{universe}} = \Delta E_{\text{sys}} + \Delta E_{\text{sur}} = 0\), meaning that the total change in energy of the system and surroundings (the universe) is zero. When the system gains or loses energy, the surroundings must lose or gain an equivalent amount of energy to maintain this conservation.

Determine the System's Change in Internal Energy

Given that the system's change in internal energy is \(\Delta E_{\text{sys}}=+65 \text{ kJ}\), this means the system has gained 65 kJ of energy.

Calculate the Surroundings' Change in Internal Energy

Since the total energy change in the universe must be zero, the surroundings must have lost the same amount of energy that the system gained. Mathematically, this is represented as \(\Delta E_{\text{sur}} = -\Delta E_{\text{sys}} = -65 \text{ kJ}\).

Choose the Correct Statement

Therefore, the true statement is that the system gains 65 kJ of energy and the surroundings lose 65 kJ of energy. This corresponds to option d.

Key concepts

First Law of Thermodynamics

When examining phenomena such as heat transfer or work done by a system, the First Law of Thermodynamics serves as a fundamental principle governing energy flow. It's a version of the law of conservation of energy, tailored for thermodynamic processes. The law asserts that the internal energy of an isolated system is constant, unless energy is added or removed by work or heat.

In its simplest formulation, the First Law can be expressed as: \[\begin{equation}\text{\(\Delta U = Q - W\)}\text{,}\text{\end{equation}\]}where \(\Delta U\) represents the change in internal energy of the system, \(Q\) is the heat added to the system, and \(W\) is the work done by the system on its surroundings. If we consider the system to gain energy, either through heat or work, the change in internal energy will be positive.

Conservation of Energy

The conservation of energy is a principle stating that energy cannot be created or destroyed, only transformed from one form to another. This is true for all isolated systems and applies across different branches of science, from mechanics to thermodynamics and beyond.

In a thermodynamic context, energy transformations involve heat and work. Even when energy appears to be 'lost', as when an object cools down, it is not destroyed but transferred to another object or converted into a different form of energy. When applying this to our everyday experience, it reminds us of the interconnectedness of energy exchanges in our environment.

For example, when a car burns fuel, the chemical energy stored in the gasoline is converted into kinetic energy, heat, and sound. Although some of the energy is dissipated, the total amount of energy is the same before and after the fuel is burned, albeit in different forms.

System and Surroundings

In thermodynamics, distinguishing between a 'system' and its 'surroundings' is crucial for analyzing energy interactions. A system denotes the part of the universe that is being studied, while the surroundings consist of everything else that can interact with the system.

The boundary separating the system from the surroundings can be real or imaginary, fixed or flexible. It's also characterized by whether it allows for the transfer of matter or energy: if it does not allow for either, we call it an isolated system; if it allows for energy but not matter, it's termed a closed system; and if it allows for both energy and matter to cross the boundary, it's an open system.

Using these concepts, we can better understand the changes a system undergoes by tracking how it exchanges energy with its surroundings. For instance, when boiling water in a pot, the pot and water combined can be considered the system, while everything outside the pot is the surroundings. As the water heats up, it gains thermal energy while the surrounding air loses it, showcasing the direct interaction between the system and surroundings according to the principles of the First Law of Thermodynamics.