# Video: Finding the Specific Heat Capacity of a Substance given the Change in Its Temperature and Internal Energy

Asphalt concrete is used to surface roads. When under direct sunlight for a long time, it can get very hot. If 2500 kg of asphalt increases in temperature from 18°C to 40°C, absorbing 50 MJ of energy from sunlight, what is the specific heat capacity of asphalt concrete? Give your answer to 2 significant figures.

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### 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.