2.8: Heat
Learning Objectives
- Define heat.
- Relate the amount of heat to a temperature change.
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:
qαm × ΔT
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 capacity, 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:
[latex]\frac{J}{g~\cdot~^{\circ}C}[/latex] or [latex]\frac{J}{g~\cdot~K}[/latex]
depending on what the unit of ΔT is. 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.
Example 2.8.1
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)(0.449 [latex]\frac{J}{g~\cdot~^\circ~C}[/latex])(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 2.8.1
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
2,260 J
Example 2.8.2
It takes 5,408 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,
5,408 J = (373 g)c(104°C)
We divide both sides of the equation by 373 g and 104°C:
c = [latex]\frac{5,408~J}{(373~g)(104~^{\circ}C)}[/latex]
Combining the numbers and bringing together all the units, we get:
c = 0.139 J/g•°C
Exercise 2.8.2
Gold has a specific heat of 0.129 J/g·°C. If 1,377 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 2.8.1, Specific Heats of Various Substances, 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 2.8.1: 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
-
Heat is the transfer of energy from one substance to another due to temperature differences between the two substances.
-
Heat can be calculated in terms of mass, temperature change, and specific heat.
