# 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?

Jun 2, 2015

You'd need +28 kJ of heat.

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

$q = m \cdot c \cdot \Delta T$, where

$q$ - the amount of heat supplied;
$m$ - the mass of the sample;
$c$ - the specific heat of wood;
$\Delta T$ - 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 ${1}^{\circ} \text{C}$. In your case, you need 2.03 J to raise the temperature of 1 g of wood by ${1}^{\circ} \text{C}$.

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 $q$

$q = 550 \cancel{\text{g") * 2.03"J"/(cancel("g") ^@cancel("C")) * (10.0-(-15))^@cancel("C}}$

$q = 550 \cdot \text{2.03 J" * 25 = "27912.5 J}$

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

$q = \textcolor{g r e e n}{\text{+28 kJ}}$

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