Changes in temperature
In this section, we will investigate how temperatures change when hot water and cold
water are mixed. In situations such as this, both the hot and the cold objects are
affected: both change temperature. To reflect the fact that two objects participate, this
process is called an interaction; specifically, a thermal interaction.
In most thermal interactions between two objects, the temperature of the hotter one
decreases and the temperature of the colder one increases. Eventually, the two
interacting objects arrive at the same intermediate temperature. The objects then
maintain constant temperature unless affected by interactions with other objects. When
two interacting objects have reached the same temperature, they are said to be in
thermal equilibrium.
Since we are interested in the interaction between hot and cold water, we do not
want any other interactions to be going on at the same time. That way, all of the
temperature changes are due to just the interaction between the hot and cold water.
Unfortunately, it is not possible to prevent all other thermal interactions entirely.
However, by conducting experiments inside a Styrofoam cup it is possible to reduce the
effects of other interactions. Styrofoam has the useful property of keeping hot things hot
and cold things cold. In terms of thermal interactions, we would say that the plastic foam
cup inhibits interactions between the surroundings and whatever is inside the cup.
In the following and all subsequent experiments, estimate
temperatures to the nearest tenth of a degree Celsius (0.1 °C).
Experiment 2.1
List several variables that you think will affect the heat transfer in the two systems.
In the next several experiments, water will be poured from one Styrofoam cup to
another. This experiment concerns the effect that pouring has on the temperature
of water.
A. Pour about 50 g of hot water (at 60°C to 70°C) from one cup to another.
Measure the temperature before and after pouring.
How much does the temperature of the water change?
B. Pour about 50 g of room temperature tap water from one cup to
another.
How much does the temperature of the water change?
C. In which case above (if either) was the temperature change smaller?
D. Suppose you are interested in the thermal interaction between hot
water and cold water and wish to minimize other interactions.
What does your answer to part C suggest about whether it is better to pour hot
water into cold water or cold water into hot water? Explain.
It is important in the following experiments to know the temperatures of the two
samples of water immediately before they are mixed. The following procedure for
mixing the water should be followed.
Procedure for mixing water samples
Record the temperature of the tap water first, since its temperature will not be changing
while it is in the cup. Hold the cup of tap water above the hot water as if you were about to
pour the first drop. Just before you actually do pour, record the temperature of the hot
water. Then immediately pour the room temperature water into the hot water. Quickly
record the temperature of the resulting mixture.
Experiment 2.2
A. Mix equal masses of hot water and tap water. Use at least 25 g of water for each
sample. Carefully note the temperature of each sample before mixing and then
note the final temperature after mixing.
Use several initial temperatures for the hot water, but do not use
temperatures higher than 60°C or the water will cool too fast in the
cup. Continue experimenting until you have a rule for predicting the
temperature of the mixture and data to support your rule.
Write a clear statement of your rule.
B. When hot and cold water are mixed, the hot water cools off and the cold water warms
up. The final temperature of both is the same. If we subtract the final temperature from
the initial temperature of the cold water, the answer will tell us how much the temperature
of the cold water changed. We can similarly calculate the temperature change of the hot
water.
Calculate the temperature changes of the hot water and of the cold water in each of
your experiments in part A.
How do the temperature changes of the hot and cold water compare?
Experiment 2.3
In this experiment, we will investigate how the masses of the samples of water affect the
final temperature of the mixture.
A. Mix various amounts of hot and room temperature water. Use at least 25 g of water
for each sample. Do not use water hotter than 60°C. Use simple mass ratios such as 2
to 1, 1 to 2, 3 to 1, 2 to 3, and so on. Do four experiments.
B. Enter your results in a table like the one below:
Mass
Hot Water
Cold Water
Initial
Final Temp. Mass Initial Final Temp.
Temp.
Temp. Change
Temp. Temp. Change
C. If two samples of water are mixed, it is possible to predict which
sample will change temperature more. How? Support your answer
with data from part A.
D. For each experiment in part A, calculate the following two quantities:
Quantity 1: the mass of the hot water times the temperature
change of the hot water.
Quantity 2: the mass of the cold water times the temperature
change of the cold water.
Plot a graph of quantity 1 versus quantity 2. That is, plot a graph of
the mass times temperature change for the hot water versus the
mass times temperature change for the cold water.
Should (0,0) be included as a data point?
E. The graph of quantity 1 versus quantity 2 should be nearly straight. Draw a
single straight line through the middle of the points.
Note: When experimental data points do not lie exactly in a
neat pattern, the usual practice is to draw a smooth curve or
line through the points. Do not draw a connect-the-dots, zigzag
line. Such a line implies that you think the measured data points
are exact, with no uncertainty. A zigzag graph indicates that the
quantities are related in a very irregular way; a smooth graph
indicates a more regular relation.
Compute the slope of the graph.
What does your result for the slope imply about the relation
between the mass times temperature change of the hot water
and the mass times temperature change of the cold water?
What does your data suggest about interpreting the statement “Heat loss = Heat
gained?” Consider different ways of defining the system.