# Calculating Heat, Energy & Temperature Changes

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• 0:05 Heat and Temperature
• 0:52 Special Heat
• 1:32 Latent Heat
• 2:27 Finishing the Problem
• 4:39 A Heating Curve
• 5:39 Lesson Summary

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Lesson Transcript
Instructor: Damien Howard

Damien has a master's degree in physics and has taught physics lab to college students.

In this lesson, we're going to learn about the relationship between heat and temperature. We'll explore how they affect each other by working through an example problem and gain insight into their relationship by learning how to read a heating curve.

## Heat and Temperature

One of the earliest concepts in thermal physics that causes confusion is the difference between heat and temperature. In our mind heat and temperature seem to mean the same thing. Physically this isn't true though. Heat is a form of energy transferred from hot substances to cold ones. Temperature is a measurement of average kinetic energy of the molecules in a system. You'll soon see these must be different, as there are times when adding heat to a system doesn't likewise increase the temperature.

In this lesson, we're going to show how heat affects temperature and phase changes in substances. Phase changes happen when a substance goes from a solid to a liquid to a gas and vice versa. We'll work through an example problem that deals with heating up substances, and learn how to read heating curves.

## Specific Heat

We're going to see how heat and temperature interact by calculating how much heat it takes to take 50 grams of -20o F ice, and turn it into 80o F water. In order to do this we're going to have to use two different energy formulas; one for specific heat and one for latent heat. The specific heat formula that you can see on your screen tells us how much added heat (Q) it takes to change a substance's temperature.

Here m is mass, Î”T is change in temperature, and c is specific heat. The specific heat is the amount of heat it takes to raise a substance's temperature by one degree Celsius.

## Latent Heat

While the specific heat formula tells us how much heat it takes to raise a substance's temperature, it does not tell us how much heat it takes to change a substance's phase. For that we use the latent heat formula.

Latent heat (l) is the heat required to change a substance's phase per unit mass. There are two different types of latent heat: latent heat of fusion and latent heat of vaporization. The former deals with a substance's change between solid and liquid, and the latter, the change between liquid and gas.

Specific and latent heat are unique to each substance. For our example, water has the following specific and latent heat values that you can see listed on your screen as we speak.

'J' stand for Joules, which are units of energy measurement. In this case, we see J/g or Joules per gram, which refers to units of heat energy disbursed over the mass of an object.

## Finishing the Problem

We use the specific and latent heat equations together when a substance's raise in temperature brings it from one phase to another. In our example, the total heat added (Qtot) would be how much heat it takes to raise the ice's temperature to the point where it melts (Qi), plus how much heat it takes to change the ice to water (Qitw), plus how much heat it takes to raise the water's temperature (Qw) to 80o F.

Before we plug in all the information for our problem we need to do one more thing. We need to convert our temperature from Fahrenheit to Celsius. In order to do this conversion, we use the following formula.

For this problem we need to convert our starting temperature of -20o F, and our ending temperature of 80o F.

Now we use all the information we've been given in the section to solve our problem.

Finally, let's make a quick note about how our temperature intervals for Î”T, or the final temperature minus initial temperature, were chosen. These temperature intervals were chosen because above 0o C ice melts. So, our heat added for ice can only be applied for -29o C to 0o C, and our heat added for water can only be applied for 0o C to 27o C.'

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