Question

Calculate \(\Delta E\) for each of the following. a. \(q=-47 \mathrm{~kJ}, w=+88 \mathrm{~kJ}\) b. \(q=+82 \mathrm{~kJ}, w=+47 \mathrm{~kJ}\) c. \(q=+47 \mathrm{~kJ}, w=0\) d. In which of these cases do the surroundings do work on the system?

Short answer

The calculated values of \(\Delta E\) are: a. \(\Delta E = 41 \mathrm{~kJ}\) b. \(\Delta E = 129 \mathrm{~kJ}\) c. \(\Delta E = 47 \mathrm{~kJ}\) The surroundings do work on the system in cases a and b.

Step-by-step solution

Case a: Calculate \(\Delta E\)

Given values: \(q = -47 \, \mathrm{kJ}\) and \(w = +88 \, \mathrm{kJ}\). Use the First Law of Thermodynamics formula: \[\Delta E = q + w\] Plug in the given values: \[\Delta E = (-47 \, \mathrm{kJ}) + (+88 \, \mathrm{kJ})\] Calculate the result: \[\Delta E = 41 \, \mathrm{kJ}\]

Case b: Calculate \(\Delta E\)

Given values: \(q = +82 \, \mathrm{kJ}\) and \(w = +47 \, \mathrm{kJ}\). Use the First Law of Thermodynamics formula: \[\Delta E = q + w\] Plug in the given values: \[\Delta E = (+82 \, \mathrm{kJ}) + (+47 \, \mathrm{kJ})\] Calculate the result: \[\Delta E = 129 \, \mathrm{kJ}\]

Case c: Calculate \(\Delta E\)

Given values: \(q = +47 \, \mathrm{kJ}\) and \(w = 0\). Use the First Law of Thermodynamics formula: \[\Delta E = q + w\] Plug in the given values: \[\Delta E = (+47 \, \mathrm{kJ}) + (0)\] Calculate the result: \[\Delta E = 47 \, \mathrm{kJ}\]

Work done by surroundings

To determine in which of these cases the surroundings do work on the system, we need to look for positive values of \(w\). Recall that: - \(w > 0\): work is done by the surroundings on the system From the given cases: - Case a: \(w = +88 \, \mathrm{kJ}\) - Case b: \(w = +47 \, \mathrm{kJ}\) - Case c: \(w = 0\) So, the surroundings do work on the system in cases a and b.

Key concepts

Internal Energy

When we talk about internal energy in the context of thermodynamics, we're referring to the energy contained within a system due to both its molecular composition and motion. Internal energy is a state function, meaning it depends only on the state of the system, not on how it reached that state.

In the First Law of Thermodynamics, internal energy (\(\Delta E\)) is expressed as the sum of heat added to the system (\(q\)) and the work done on the system (\(w\)).

• In increase in internal energy indicates energy has been absorbed by the system.
• A decrease signifies that energy has been released to the surroundings.

This balance between heat and work essentially 'knocks the dominoes' of thermodynamic processes like metabolism, engine operations, and chemical reactions.

Heat

Heat in thermodynamics refers to the energy that transfers between a system and its surroundings due to a temperature difference. Whenever there's a heat flow, it suggests that energy is being transferred from something warmer to something cooler.

Heat is traditionally measured in joules, but it's often expressed in kilojoules (kJ) within thermodynamics to simplify understanding.

• A positive heat value (\(q > 0\)) indicates that the system is absorbing heat from its surroundings.
• A negative heat value (\(q < 0\)) suggests heat is being released by the system.

In essence, understanding how heat works helps us manage energy flows, whether it's for warming our homes or understanding the thermal efficiency of engines.

Work

In thermodynamics, work is the process through which energy is transferred from one system to another, apart from energy transfer due to temperature differences. Think of work as the energy needed to move an object against a force, like pushing a block against friction on a table.

The concept of work in thermodynamics is crucial because it tells us how interactions with the surroundings affect the system.

• Work is positive (\(w > 0\)) when work is done on the system, as seen in cases where the surroundings exert a force.
• It is negative (\(w < 0\)) when the system does work on the surroundings.

By understanding work, we can better comprehend processes like compression or expansion in engines, and how these impact the total energy of the system.

Thermodynamic System

A thermodynamic system is essentially any defined space or quantity of matter upon which we wish to focus our study of energy changes. This system idea helps to understand the flow of energy as it is exchanged with its surroundings.

Systems can be classified into different types:

• Open systems, which can exchange both energy and matter with their surroundings.
• Closed systems, which can exchange only energy.
• Isolated systems, which do not exchange any energy or matter.

For students learning thermodynamics, visualizing the system's boundaries helps grasp concepts like energy conservation and transfer, and how changes in heat and work manifest as changes in internal energy.