# 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?

##### 1 Answer

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

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 themassof the sample#c# is thespecific heatof the substance#DeltaT# is thechange in temperature, defined as the difference between thefinal temperatureand theinitial temperatureof 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.