How much heat is needed to increase the temperature of "1 kg"1 kg of foam by "2 K"2 K knowing that the specific heat of foam is "1200 J kg"^(-1)"K"^(-1)1200 J kg1K1 ?

1 Answer
Jan 27, 2017

"2400 J"2400 J

Explanation:

The specific heat of a substance tells you how much heat is needed in order to increase the temperature of one unit of mass of that substance, usually "1 g"1 g, by 1^@"C"1C or by "1 K"1 K.

In your case, the specific heat of foam is given as "1200 J kg"^(-1)"K"^(-1)1200 J kg1K1, which means that one unit of mass is "1 kg"1 kg. You can thus say that in order to increase the temperature of "1 kg"1 kg of foam by "1 K"1 K, you must provide it with "1200 J"1200 J of heat.

Now, you must figure out how much heat is needed to increase the temperature of "1 kg"1 kg of foam by "2 K"2 K.

In this case, you know that you need "1200 J"1200 J to increase its temperature by "1 K"1 K, so you can say that another "1200 J"1200 J will increase its temperature by "1 K"1 K again.

In other words, you will need

2 color(red)(cancel(color(black)("K"))) * overbrace("1200 J"/(1color(red)(cancel(color(black)("K")))))^(color(blue)("needed for 1 kg of foam")) = color(darkgreen)(ul(color(black)("2400 J")))

I'll leave the answer rounded to two sig figs.