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© 2014 Pacific Crest
101
M
aking it Matter
Solving problems in your life
●
What GPA do you need this term to increase your GPA by 0.3?
●
Calculate your contribution to rent, utilities, food and other costs, assuming you share a house with
four other students. Use average costs for these things, for your area (that information is available
online) and either assume the other individuals have the same income you do or that between the
four of you, you have income equivalent to twice the medium income for your area.
●
In chemistry you are given an equation that allows you to calculate energy used (in joules) needed
to change the temperature (in degrees centigrade) of a substance (measured in grams), if you know
the specific heat capacity of that substance. (The specific heat capacity of any substance is defined
as the amount of energy needed to increase the temperature of 1 g of the substance by 1 °C. Water’s
heat capacity is 4.184 J/g °C.)
Energy = ΔT × m × c
s
Energy = energy used (in J)
ΔT = change in temperature (in °C)
m = mass of the substance (in g)
c
s
= specific heat capacity (J/g °C)
You are now given a set of challenges:
a. Determine how much energy is needed to increase the temperature of 400 grams of water by
20 degrees centigrade.
b. What is the specific heat capacity of a mystery substance if it takes 298.5 J to change the
temperature of 30 grams of the substance by 10 °C?
c. Given substance Q, how much has its temperature increased if you have
x
grams of it and
applied
y
joules of energy?
d. How many grams of Q can we heat by 10 degrees if we have
z
joules of energy to apply to it?
L
earning to Learn Mathematics
Reflecting on and appreciating your learning
1. Of the information presented in this activity, what was new? What did you already know that helped
you learn to solve equations?
2. What is the danger of not knowing limitations in the use of a methodology (e.g., misuse of a property
in isolating a variable)?
3. How do you focus on the key object when the context is confusing (e.g., when notation is new or
complex such as in the literal equation example (
Model 2
)?
2.4 Solving an Equation