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)# ?

Question

Wyatt Adkins · Accepted Answer

#"2400 J"#

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"#, by #1^@"C"# or by #"1 K"#.

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

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

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

Wyatt Atkins · Answer

undefined To calculate the heat needed to increase the temperature of 1 kg of foam by 2 K, you would use the formula:

Heat = mass × specific heat × temperature change

Substituting the given values:

Heat = 1 kg × 1200 J kg^(-1) K^(-1) × 2 K

Heat = 2400 J