Questions about specific heat capacity?

Question

A:

Calculate the amount of thermal energy required to raise the temperature of 3.0 kg of aluminum from 20.0 degrees celcius to 80.0 degrees celcius. The theoretical specific heat capacity of aluminum is 0.897 gram degrees celcius.

B:

The theoretical specific heat capacity of water is 4.19 J/g’C. Aluminum has a theoretical specific heat capacity of 0.897 J/g’C. If 100g of water and 1.00 g of aluminum are both heated to 50.0’C, which substance will contain the greater quantity of thermal energy?

C:

When 60.0 joules of thermal energy is added to a mass of copper, the temperature of the copper increases by 10.4 degrees celcius. The specific heat capacity of copper is 0.385 joules per gram degrees celcius. What mass of copper was heated?

I know my formulas and all, but what do I plug in and how do I solve it?(So far, I've only dealt with the specific heat capacity of water and not of metals)

Thank you for your time.

Answer 1

A. The specific heat is incorrectly stated; the units of heat measure are not specified.   It IS correctly stated in problem B, and using that value, we get (80-20)(3000)(0.897) joules.  You do the arithmetic.

B. Water, of course; not only is there more of it, but it has a larger specific heat.  But the expression "contains more thermal energy" is flawed; it should read "has had more thermal energy added."

C.  Since the heat added is proportional to the mass, to the temp change, and to the specific heat, we have 60 = m (10.4)(0.385).  Rearrange, and solve for m; the result is in grams.

Answer 2

Above answer is correct. to address your problem, learn about "dimensional analysis"

for example, it allows me to solve these problems without knowing any formulas at all.

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In case you are not familiar: Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving a mix of different kinds of physical quantities. It is routinely used by physical scientists and engineers to check the plausibility of derived equations and computations. It is also used to form reasonable hypotheses about complex physical situations that can be tested by experiment or by more developed theories of the phenomena.

Basically it is used to check that you have an equation, with actual measurements, correct. Write all the units down, and cancel and combine them, and the result should have the correct units for the answer.

Or if you are unsure how to combine measurements to get the answer desired, arrange the elements of the calculation so that the units combine to form the desired result.

take an example.

Specific heat has units of J/(g·K). I have one quantity of energy in 10 J, a temperature in 5C (same as K) and a weight in 15grams.

So if I take the energy and divide it by the temp and weight, I'll get the correct units.

or

10J / (5C*15g) = specific heat in J/(g·K)

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