How do you calculate the specific heat capacity of a piece of wood if 1500.0 g of the wood absorbs #6.75 * 10^4# joules of heat, and its temperature changes from 32°C to 57°C?

1 Answer
Jan 29, 2016

Answer:

#1.8"J"/("g" ""^@"C")#

Explanation:

A substance's specific heat tells you how much heat much either be added or removed from #"1 g"# of that substance in order to cause a #1^@"C"# change in temperature.

The equation that establishes a relationship between specific heat, heat added or removed, and change in temperature looks like this

#color(blue)(q = m * c * DeltaT)" "#, where

#q# - the amount of heat added / removed
#m# - the mass of the sample
#c# - the specific heat of the substance
#DeltaT# - the change in temperature

In your case, the #"1500.0-g"# piece of wood is said to absorb a total of #6.75 * 10^4"J"# of heat. This caused its temperature to increase from #32^@"C"# to #57^@"C"#.

The difference between the final temperature and the initial temperature of the sample will be the value for #DeltaT#.

#DeltaT = 57^@"C" - 32^@"C" = 25^@"C"#

This means that the specific heat of the wood is equal to

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

Plug in your values to get

#c = (6.75 * 10^4"J")/("1500.0 g" * 25^@"C") = color(green)(1.8"J"/("g" ""^@"C"))#

The answer is rounded to two sig figs, the number of sig figs you have for the two temperatures of the sample.