Question

The specific heat of wood is 2.03 J/g C. How much heat is needed to raise the temperature of 550 g of wood from -15.0 C to 10.0 C?

Answer 1

You'd need +28 kJ of heat.

The equation that establishes a relationship between supplied heat and increase in temperature looks like this

`q = m * c * DeltaT`, where

`q` - the amount of heat supplied;
`m` - the mass of the sample;
`c` - the specific heat of wood;
`DeltaT` - the change in temperature, defined as the difference between the final temperature and the initial temperature.

A substance's specific heat tells you how much heat is needed to raise the temperature of 1 gram by `1^@"C"`. In your case, you need 2.03 J to raise the temperature of 1 g of wood by `1^@"C"`.

SInce you have more than 1 gram of wood and the temperature change is larger than 1 degree Celsius, you'll of course require a significant amount of heat.

Plug your values into the equation and solve for `q`

`q = 550cancel("g") * 2.03"J"/(cancel("g") ^@cancel("C")) * (10.0-(-15))^@cancel("C")`

`q = 550 * "2.03 J" * 25 = "27912.5 J"`

Rounded to two sig figs, the number of sig figs you gave for the mass of the sample, and expressed in kilojoules, the answer will be

`q = color(green)("+28 kJ")`

SIDE NOTE The + sign mens that heat is supplied to the sample.