The specific heat of steel is 420 J/(kg°C). How much energy is required to heat 1 kg of steel by 20 °C?

Question

The specific heat of steel is 420 J/(kg°C).  How much energy is required to heat 1 kg of steel by 20 °C?

Naomi Aronson · Accepted Answer

#"8400 J"#

The specific heat of a substance tells you how much heat is required in order to heat one unit of mass, usually #"1 g"#, of that substance by #1^@"C"#.

In this case, the specific heat of steel uses #"1 kg"# as the unit of mass, which means that the value given to you tells you how much heat is required in order to heat #"1 kg"# of steel by #1^@"C"#.

Since you have

#c = "420 J kg"^(-1)""^@"C"^(-1)#

you can say that you need #"420 J"# of heat in order to increase the temperature of #"1 kg"# of steel by #1^@"C"#.

This means that in order to increase the temperature of a given mass of steel by #20^@"C"#, you'd need

#20 color(red)(cancel(color(black)(""^@"C"))) * "420 J"/("1 kg" color(red)(cancel(color(black)(""^@"C")))) = "8400 J kg"^(-1)#

For #"1 kg"#, this gives you

#1 color(red)(cancel(color(black)("kg"))) * "8400 J"/(1color(red)(cancel(color(black)("kg")))) = color(darkgreen)(ul(color(black)("8400 J")))#

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

Peyton Adams · Answer

undefined The energy required to heat 1 kg of steel by 20°C is 8,400 J.