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

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.