### Video Transcript

Asphalt concrete is used to surface
roads. When under direct sunlight for a
long time, it can get very hot. If 2500 kilograms of asphalt
increases in temperature from 18 degrees Celsius to 40 degrees Celsius, absorbing 50
megajoules of energy from sunlight, what is the specific heat capacity of asphalt
concrete? Give your answer to two significant
figures.

Okay, so say we have this huge slab
of asphalt. We’re told it has a mass of 2500
kilograms and that this mass is heating up in the sun. Thanks to all the energy it absorbs
from the sun, the asphalt goes from a temperature of 18 degrees Celsius to 40
degrees Celsius. That tells us that the change in
temperature undergoes or we can call Δ𝑇 is equal to 40 degrees Celsius minus 18
degrees Celsius or 22 degrees Celsius. We’re told that the amount of
energy the asphalt absorbs in order to effect this change in temperature is 50
megajoules. That’s 50000000 joules of
energy.

Based on all this information, we
want to solve for the specific heat capacity of asphalt concrete. At this point, we can recall that
specific heat capacity is the amount of energy needed to increase the temperature of
one kilogram of a given material by one degree Celsius. As a mathematical equation, we can
say that this amount of energy — what we can call 𝐸 — is equal to the mass of our
substance multiplied by the specific heat capacity multiplied by the change in
temperature of the substance, Δ𝑇.

Like we said, it’s the specific
heat capacity 𝑐 that we want to solve for in this case. So to do that, let’s rearrange this
equation algebraically. Let’s divide both sides of the
equation by the mass of our substance multiplied by its change in temperature. When we do that, we find the
specific heat capacity is equal to the energy added into our material divided by the
mass of that material multiplied by its change in temperature.

In our case, we know the mass of
our substance. It’s given as 2500 kilograms. We also know its change in
temperature. We calculated that to be 22 degrees
Celsius. And moreover, we know the amount of
energy input to our substance, 50000000 joules. So to calculate specific heat
capacity, it’s just a matter of substituting in these values into this
expression. When we do that, our mass of 2500
kilograms and our change in temperature of 22 degrees Celsius can go straight in as
is.

But our input energy, 50
megajoules, needs to change a bit. That’s because mega is a prefix
that means million. So to express our energy in base
units of joules, we need to convert it from 50000000 joules and write it as 50 times
10 to the six joules. With this conversion done, we can
see that the final units of our specific heat capacity will be joules per kilogram
degrees Celsius, just what we want. When we calculate this value to two
significant figures, we find a result of 910 joules per kilogram degrees
Celsius.

This answer means that in order to
heat one kilogram of asphalt concrete by one degree Celsius, we would need to input
910 joules to the concrete. That’s the specific heat capacity
of the asphalt.