Video Transcript
Which of the following equations
can be used with the results from a calorimetry experiment to calculate the heat
energy transferred during a chemical reaction? (A) 𝑞 equals parentheses 𝑐 times
Δ𝑇 divided by 𝑚. (B) 𝑞 equals 𝑚 divided by 𝑐
times Δ𝑇. (C) 𝑞 equals 𝑚 times 𝑐 times
Δ𝑇. (D) 𝑞 equals 𝑐 divided by 𝑚
times Δ𝑇. Or (E) 𝑞 equals parentheses 𝑚
times 𝑐 divided by Δ𝑇.
Calorimetry is the study of heat
transferred during physical and chemical changes, where heat is the flow of thermal
energy due to a difference in temperature, where temperature is a measure of the
average kinetic energy of matter in a system. It can also express how hot or cold
a substance is. So, heat and temperature are
different.
Heat energy is given the symbol 𝑞
and is measured in units of joules, whereas temperature is given the symbol capital
𝑇 and is measured in units of degrees C or kelvin. An example to show the difference
between heat and temperature is heating water in a saucepan. The burner provides a source of
heat. The heat energy is transferred to
the water in the saucepan. This causes the kinetic energy to
increase, causing the water to boil. Therefore, there is an increase in
temperature.
The temperature can be measured
using a thermometer. The extent to which the temperature
increases depends on the heat capacity of the substance, where the heat capacity is
the ratio of the amount of heat energy transferred to an object to the resulting
increase in its temperature. The heat capacity, given the symbol
capital 𝐶, is thus equivalent to 𝑞, the amount of heat energy transferred, divided
by Δ𝑇, the temperature change. And capital Δ means difference or
change in.
Heat energy has units of joules,
and either degrees Celsius or kelvin can be used for the temperature change. The size of one degree Celsius and
one degrees kelvin are the same. Therefore, a temperature change in
both units is equal. Heat capacity has the units joules
per kelvin or joules per degree Celsius. So, we have the equation for the
heat capacity, but the heat capacity doesn’t consider the mass of the object being
heated up. The specific heat capacity is the
quantity of energy in joules required to raise the temperature of one gram of a
substance by one degree Celsius. It is given the symbol lowercase
𝑐, and it is calculated by dividing the heat capacity by the mass of the
object.
Let’s clear a little space and look
at this more closely. As previously stated, the units for
heat capacity are joules per kelvin or joules per degree Celsius. Although the unit kilograms is
often used for mass, grams are often used instead when speaking of specific heat
capacity. So, the units for specific heat
capacity are joules per gram per degree Celsius.
We now have the two key equations
that we need to solve this question. The question asks us how we
calculate the heat energy. So, we need to make 𝑞, heat
energy, the subject. We can make 𝑞 the subject by
multiplying both sides of the equation by Δ𝑇. The Δ𝑇’s on the right side of the
equation cancel, leaving us with 𝑞 equals capital 𝐶, the heat capacity, multiplied
by Δ𝑇. We then need to substitute capital
𝐶, the heat capacity, with the lowercase 𝑐, the specific heat capacity, and 𝑚,
the mass.
First of all, we need to rearrange
this equation to make capital 𝐶 the subject. If we multiply both sides of the
equation by 𝑚, then the 𝑚’s on the right side of the equation will cancel, leaving
us with capital 𝐶 equals 𝑚 times lowercase 𝑐. If we substitute the capital 𝐶 in
this equation with 𝑚 times 𝑐, we get 𝑞 equals 𝑚 times 𝑐 times Δ𝑇, where 𝑞 is
the heat energy, 𝑚 is the mass, Δ𝑇 is the temperature change, and lowercase 𝑐 is
the specific heat capacity.
The specific heat capacity of an
object affects the amount of heat energy that’s required to heat it up. For example, water has a higher
specific heat capacity than sand, so it takes more energy to heat up than land
does. That’s why when it’s warm, the sand
on a beach will be hot, but the seawater will be cold. Therefore, the answer to the
question “Which of the following equations can be used to calculate the heat
energy?” is (C) 𝑞 equals 𝑚 times 𝑐 times Δ𝑇.
