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?

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.