What is the specific heat of an unknown substance if 2000 J of energy are required to raise the temperature of 400 grams of the substance 45 degrees Celsius?

1 Answer
May 28, 2016

Answer:

#"0.1 J g"^(-1)""^@"C"^(-1)#

Explanation:

A substance's specific heat tells you how much heat is needed in order to raise the temperature of #"1 g"# of that substance by #1^@"C"#.

Your tool of choice here will be this equation

#color(blue)(|bar(ul(color(white)(a/a)q = m * c * DeltaTcolor(white)(a/a)|)))" "#, where

#q# - the amount of heat gained
#m# - the mass of the sample
#c# - the specific heat of the substance
#DeltaT# - the change in temperature, defined as the difference between the final temperature and the initial temperature

In your case, the sample is said to have a mass of #"400 g"#. The change in temperature is said to be equal to #45^@"C"#.

You know that in order to increase the temperature of this sample by #45^@"C"#, you need to provide it with #"2000 J"# of energy, which means that its specific heat will be

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

#c = "2000 J"/("400 g" * 45^@"C") = color(green)(|bar(ul(color(white)(a/a)color(black)("0.1 J g"^(-1)""^@"C"^(-1))color(white)(a/a)|)))#

The answer is rounded to one sig fig.