If told the temperature outside we have an idea of how hot or cold it is. Told the temperature is 10 degrees Fahrenheit we know that it wil be cold outside, 95 degrees Fahrenheit we are prepared for hot. Temperature is a measure of the degree of hotness or coldness of an object, sample, whatever. Degrees Fahrenheit, Celsius or kelvin are units which associated with a number communicate temperature.

If told to heat some water, we would place a container of water on the stove and turn on the gas, or electricity on the stove and heat the water. Or we might place the container (not metal) into a mircowave oven and heat the sample that way. Heating consists of placing a sample at a lower temperature in contact with a sample at a higher temperature. Heat than flows from higher temperature to lower temperature. Joules or calories (kilocalories) are units which are associated with heat.

We have some additional inituition about heat and temperature. Suppose we had two samples of water each in a beaker, one sample weighed 100. grams the other weighed 25.0 g. Both the samples are at 25.0 ÐC. If we added the same amount of heat to both samples which will attain the higher temperature? The 100. gram or the 25.0 gram sample? Answer.

Our intuition is that adding the same amount of heat to two samples the one with the smaller mass will have the higher final temperature. This is an inverse relationship. Such a relationship is associated with changes that are opposite, i.e., increasing one parameter causes a decrease in the other. A direct relationship is apparent when increasing one parameter causes an increase in the other. So a change in temperature is inversely related to the mass of the substance. When adding the same amount of heat to different masses of the same substance we can determine the change in temperature using the mathematical relationship.

So we see from above adding heat to samples of water cause an increase in temperature of the sample. Consider what happens when the same amount of heat is added to two different substances. If the same amount of heat is added to a sample of ethyl alcohol and a sample of water (both with the same mass) the temperature change is different! This may be a surprise. A sample of water will have a change in temperature almost twice that experienced by ethyl alcohol. It turns out that ethyl alcohol and have different capacities to hold heat. So it appears that when a sample of a substance absorbs heat the temperature change we observe depends on an additional factor besides the mass of the sample. The additional factor is called the specific heat. This is a physical property which is unique for each pure substance. Water has one of the highest specific heats.

So what is a specific heat? It is defined as the amount of heat required to change the temperature of 1 gram of a substance by 1 degree Celsius. What are some typical values for specific heat? Look at the table below.

So how do we use this specific heat property? We can use it to understand how much heat is required to change the temperature of a sample of a substance. Lets look at several problems which use the concept of specific heat. Notice the units in the column of specific heats. The units on specif heat are J, joules, per gram degree Celsius, or J ­ g^-1 ­ C^-1. We recognize grams as a mass unit and degrees Celsius as a temperature unit. Joules is the strange unit. Joules are associated with heat. When we add heat to water by heating it on the stove or microwave the units are joules. Everyone must be careful not to confuse degrees Celsius as a heat unit, it is not! Heat is measured in joules. A unit of heat (energy) you have heard of is Calories. Joules are related to Calories. They are not the same but they are related by a conversion factor.

In the above problems we are solving for one of the variables in the equation,

Fairly straight forward application. Now lets look at something a little more interesting. Lets return to the one of the problems we started this section with.

Given two samples of water each weighing 100 g one is at a temperature of 50.0 degrees Celsius, the other at 25.0 degrees Celsius. When mixed together what is the final temperature? In this problem we have a slightly different question. How do we approach this problem using hte relationship that we used in the previous problems?

The trick is to recognize how heat flows. The sample of water at 50 °C contains a certain amont of heat. When it is added to the sample of water at the lower temperature heat will flow from the water at 50 °C to the water at 25 °C. The heat lost by the warm water will be gained by the cool water. How do we express that equality?

heat_hot = –heat_cool

This equality says exactly what we said above, the minus sign reflects the opposite direction of the heat flow for the cool water. While this equality explains how heat flows, it does not answer our question. To solve the problem we must substitute for heat using the relationship between heat and specific heat, so substituting yields,

Now we substitute in the quanities given in the problem and solve. The mass of the hot and cool water were the same...100 g and the specific heat for water is 4.184 J ­ g^-1 ­ °C^-1. Substituting we have,

Notice the specific heat and the mass of the samples cancel, leaving,

Now we replace the temperature information,

The initial temperature, (T_i)_hot, for the hot water is 50 °C, and the initial temperature, (T_i)_cool, for the cool water is 25 °C. The final temperature for the hot water and the cool water is the same because we are mixing the two samples together. So substituting,

(T_f - 50 °C) = –(T_f - 25 °C)

Collecting terms on opposite sides,

2T_f = 75 °C

T_f = 37.5 °C