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

Jan 27, 2017

$\text{2400 J}$

#### 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 $\text{1 g}$, by ${1}^{\circ} \text{C}$ or by $\text{1 K}$.

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

Now, you must figure out how much heat is needed to increase the temperature of $\text{1 kg}$ of foam by $\text{2 K}$.

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

In other words, you will need

$2 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{K"))) * overbrace("1200 J"/(1color(red)(cancel(color(black)("K")))))^(color(blue)("needed for 1 kg of foam")) = color(darkgreen)(ul(color(black)("2400 J}}}}$

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