5.1

Energy: Basic Principles

Energy is defined as the capacity to do work or produce heat. Two operational sub-categories are routinely singled out:

• Work-energy – the energy required to move an object that possesses mass.
• Heat-energy – the energy required to raise the temperature of matter.

Two practical units dominate quantitative work:

• Joule (J): the SI unit derived from the kinetic energy of a 2\,\text{kg} mass moving at 1\,\text{m s}^{-1} (i.e. 1\,\text{J}=1\,\text{kg m}^{2}\text{s}^{-2}).
• Calorie (cal): the energy needed to raise the temperature of 1\,\text{g} of water by 1\,^{\circ}\text C.
1\,\text{cal}=4.184\,\text{J}.

Thermodynamics and Thermochemistry

Thermodynamics is the broad study of energy and its transformations. Thermochemistry narrows that focus to the heat flow that accompanies chemical reactions or phase changes.

Conservation of Energy

The Law of Conservation of Energy states that energy can neither be created nor destroyed. It can, however, be converted from one form to another.

System and Surroundings

When studying energetic changes, a well-defined part of the universe is isolated and labelled the system; everything else constitutes the surroundings. Describing energy flow always requires specifying which is which.

Internal Energy and the First Law

Internal energy U is the total of all kinetic and potential energy contained within a system. For any change
\Delta U = q + w
where
• q is heat transferred to (positive) or from (negative) the system, and
• w is work done on (positive) or by (negative) the system.

Example (First-Law Application). A system absorbs 140\,\text J of heat and does 85\,\text J of work on the surroundings:
q = +140\,\text J;\; w = -85\,\text J;\; \boxed{\Delta U = 55\,\text J}.

Sign Conventions (summary)

• q>0 – heat absorbed by the system; q<0 – heat released. • w>0 – work done on the system; w<0 – work done by the system.

Thermal Equilibrium

Heat always flows spontaneously from a hotter object to a colder object until both reach the same temperature (thermal equilibrium).

Endothermic and Exothermic Processes

• Endothermic: heat flows from surroundings to system; the system’s energy increases while the surroundings’ energy decreases.
• Exothermic: heat flows from system to surroundings; the system’s energy decreases while the surroundings’ energy increases.

Heat Capacity Concepts

The amount of heat needed to change temperature depends on (i) mass, (ii) magnitude of temperature change, and (iii) identity of the material.

• Heat capacity C – heat required to raise the temperature of an OBJECT by 1\,\text K.
• Specific heat capacity Cp (or Cv) – heat required to raise 1\,\text g of a substance by 1\,\text K.
• Molar heat capacity C_{\text{molar}} – heat required to raise 1\,\text{mol} of substance by 1\,\text K (metals cluster near 25\,\text{J mol}^{-1}\text K^{-1}).

Raising heat capacity raises the heat required for a given temperature change.

Table highlights (representative values):
• Cp(\text{Al}) = 0.897\,\text{J g}^{-1}\text K^{-1} (molar 24.2\,\text{J mol}^{-1}\text K^{-1}). • Cp(\text{Cu}) = 0.385\,\text{J g}^{-1}\text K^{-1}.
• Cp(\text{H}2\text O, \ell) = 4.184\,\text{J g}^{-1}\text K^{-1} (molar 75.4\,\text{J mol}^{-1}\text K^{-1}).

Specific Heat – Conceptual Example

Supplying identical heat to 100\,\text g