This is "Unit 3", section 3.3 from the book General Chemistry (v. 1.0).

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3.3 Heat

Learning Objectives

  1. To know the definitions of energy and work and the associated units.
  2. To know a definition for heat and distinguish heat from temperature.
  3. To know the definition of specific heat.
  4. To be able to calculate the amount of heat associated with various physical and chemical changes.

EnergyThe ability to do work. is the ability to do work. Work (w) itself is defined as a force (F) operating over a distance (Δx):

w = F × Δx

In SI, force has units of newtons (N), while distance has units of meters. Therefore, work has units of N•m. This compound unit is redefined as a jouleThe SI unit of energy. (J):

1 joule = 1 newton•meter 1 J = 1 N•m

Because energy is the ability to do work, energy is also measured in joules.

How much is 1 J? It is enough to warm up about one-fourth of a gram of water by 1°C. It takes about 12,000 J to warm a cup of coffee from room temperature to 50°C. So a joule is not a lot of energy. It will not be uncommon to measure energies in thousands of joules, so the kilojoule (kJ) is a common unit of energy, with 1 kJ equal to 1,000 J.

An older, but still common, unit of energy is the calorie. The calorie (cal) was originally defined in terms of warming up a given quantity of water. The modern definition of calorie equates it to joules:

1 cal = 4.184 J

One area where the calorie is used is in nutrition. Energy contents of foods are often expressed in calories. However, the calorie unit used for foods is actually the kilocalorie (kcal). Most foods indicate this by spelling the word with a capital "C" Calorie. Figure 3.3(a), below, shows one example. So be careful counting calories when you eat!

Figure 3.3(a) Nutrition Label

Image Credit: By Rorybowman (here) [Public domain], via Wikimedia Commons

Heat is another aspect of energy. HeatThe transfer of energy from one body to another due to a difference in temperature. is the transfer of energy from one body to another due to a difference in temperature. For example, when we touch something with our hands, we interpret that object as either hot or cold depending on how energy is transferred: If energy is transferred into your hands, the object feels hot. If energy is transferred from your hands to the object, your hands feel cold. Because heat is a measure of energy transfer, heat is also measured in joules.

For a given object, the amount of heat (q) involved is proportional to two things: the mass of the object (m) and the temperature change (ΔT) evoked by the energy transfer. We can write this mathematically as

q ∝ mΔT

where ∝ means "is proportional to." To make a proportionality an equality, we include a proportionality constant. In this case, the proportionality constant is labeled c and is called the specific heat capacityThe proportionality constant between heat, mass, and temperature change; also called specific heat., or, more succinctly, specific heat:

q = mcΔT

where the mass, specific heat, and change in temperature are multiplied together. Specific heat is a measure of how much energy is needed to change the temperature of a substance; the larger the specific heat, the more energy is needed to change the temperature. The units for specific heat are Jg•°C. You may note a departure from the insistence that temperature be expressed in Kelvin. That is because a change in temperature has the same value whether the temperatures are expressed in degrees Celsius or kelvins.

Video: The presenter heats a weighed sample of cadmium metal in a boiling hot water bath and places it into a vessel containing a measured quantity of room temperature water. The final temperature of the formerly room temperature water is recorded. The specific heat of cadmium is calculated. Video Credit: Part of NCSSM CORE collection: http://www.dlt.ncssm. Please attribute this work as being created by the North Carolina School of Science and Mathematics. This work is licensed under Creative Commons CC-BY https://creativecommons.org/licenses/by/3.0/ via YouTube

Example 3.3-1

Calculate the heat involved when 25.0 g of Fe increase temperature from 22°C to 76°C. The specific heat of Fe is 0.449 J/g•°C.

Solution

First we need to determine ΔT. A change is always the final value minus the initial value:

ΔT = 76°C - 22°C = 54°C

Now we can use the expression for q, substitute for all variables, and solve for heat:

q=(25.0 g)(0.449 J g•°C)(54°C)= 610 J

Note how the g and °C units cancel, leaving J, a unit of heat. Also note that this value of q is inherently positive, meaning that energy is going into the system.

Exercise

Calculate the heat involved when 76.5 g of Ag increase temperature from 17.8°C to 144.5°C. The specific heat of Ag is 0.233 J/g•°C.

Answer

2260 J

As with any equation, when you know all but one variable in the expression for q, you can determine the remaining variable by using algebra.

Example 3.3-2

It takes 5408 J of heat to raise the temperature of 373 g of Hg by 104°C. What is the specific heat of Hg?

Solution

We can start with the equation for q, but now different values are given, and we need to solve for specific heat. Note that ΔT is given directly as 104°C. Substituting,

5408 J = (373 g)c(104°C)

We divide both sides of the equation by 373 g and 104°C:

c=5408 J(373 g)(104 °C)

Combining the numbers and bringing together all the units, we get

c=0.139Jg•°C

Exercise

Gold has a specific heat of 0.129 J/g• °C. If 1377 J are needed to increase the temperature of a sample of gold by 99.9°C, what is the mass of the gold?

Answer

107 g

Table 3.3(1) lists the specific heats of some substances. Specific heat is a physical property of substances, so it is a characteristic of the substance. The general idea is that the lower the specific heat, the less energy is required to change the temperature of the substance by a certain amount.

Table 3.3(1) Specific Heats of Various Substances

Substance Specific Heat (J/g• °C)
water 4.184
iron 0.449
gold 0.129
mercury 0.139
aluminum 0.900
ethyl alcohol 2.419
magnesium 1.03
helium 5.171
oxygen 0.918

Key Takeaways

  • Energy is the capacity to do work.
  • Heat is the transfer of energy due to temperature differences.
  • Heat can be calculated in terms of mass, temperature change, and specific heat.