What is the specific heat of the substance?

Question

An unknown substance weighing 34.7 g was heated from 10.2°C to 68.9°C. In this process, the substance absorbed 788 J of energy. What is the specific heat of the substance? 

Answer 1

q = mC∆T

q = heat = 788 J

m = mass = 34.7 g

C = specific heat = ?

∆T = change in temperature = 68.9º - 10.2º = 58.7º

Solving for C...

C = q / (m)(∆T) = 788 J / (34.7 g)(58.7º)

C = 0.387 J/gº

Answer 2

Hello, Angel,

The units of specific heat help guide us on how to answer this question. You really don't even need an equation.

Specidic heat is defined as the amount of energy it takes to raise a unit (g, kg, mole, etc) of a substance by 1 degree (C, K, or F). A typical unit might look like this:

J/gC

The SI standard for this unit is J/(kg*K). but you will often see terms such as kJ/mole*K, or Calories/kg*C, as well as many others. Although the numbers are different, they are all numerically equivalent.

In this case we find that 788 Joules was absorbed by 34.7 grams of the unknown substance in the process of heating it by (68.9-10.2 = 58.7 C) degrees.

To get J/(gC), we divide the 788 Joules by the product of the mass times the temperature change:

788 J/((34.7 grams)*(58.7C)) = 0.487 J/gC

It takes 0.387 Joules of energy to raise 1 gram of this substance by 1 C.

One can look up this specific heat on a table to find a possible identity of the substance. For Manganese, the specific heat is 0.479 J/gC. This is too different to be the substance, but Zinc at 0.388 J/gC sounds like a good bet. If I were smart, I'd have looked up specific heats for silver, gold, platinum, and titanium before anything else. (You might check for yourself).

Bob