Question

An unknown substance has a mass 26.3 g. The temperature of the substance increases by 11.9 degrees C when 73.5 J of heat is added to the substance. What is the most likely identity of substance?

Answer 1

Silver.

Explanation:

The idea here is that you need to use the information provided by the problem to calculate the specific heat of the substance.

Once you know this value, you can compare it to listed specific heat values of known substances and see if you can get a match.

So, the specific heat of a substance is a measure of the amount of heat needed to increase the temperature of `"1 g"` of that substance by `1^@"C"`.

You can calculate the specific heat of a substance by using the equation

`color(blue)(ul(color(black)(q = m * c * DeltaT)))`

Here

• `q` is the heat lost or gained by the substance
• `m` is the mass of the sample
• `c` is the specific heat of the substance
• `DeltaT` is the change in temperature, defined as the difference between the final temperature and the initial temperature of the sample

Rearrange this equation to solve for the specific heat of the substance

`q = m * c * DeltaT implies c = q/(m * DeltaT)`

Plug in your values to find

`c = "73.5 J"/("26.3 g" * 11.9^@"C") = "0.235 J g"^(-1)""^@"C"^(-1)`

This specific heat is actually very close to the value listed for silver

`c_"silver" = "0.233 J g"^(-1)""^@"C"^(-1)`

http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/sphtt.html

so you can conclude that your unknown substance could very well be silver.