Steel has a specific heat of 0.466 J/g Celsius . How many Joules of heat are needed to raise the temperature of 30.0 grams of steel from 42.0 Celsius to 73.3 Celsius ?

Answer 1

q = mC∆T

q = heat = ?

m = mass = 30.0 g

C = specific heat = 0.466 J/gº

∆T = change in temperature = 73.3º - 42.0º = 31.3º

q = (30.0 g)(0.466 J/gº)(31.3º)

q = 438 J (3 sig. figs.)

Answer 2

Hello, Emily,

Look at the units for the specific heat of steel: 0.466 J/gºC

This unit tells us that if we add 0.466 Joules to 1 gram of steel, it will raise it's temperature by 1 ºC.

If we have 30 grams, we'd need 30x(0.466 J) to go up 1 ºC, and if we have more than a gram, we need to multiply the unit by the number of grams present. The unit of specific heat, J/gºC, helps guide us through the calculations.

In this case we have 30 grams of steel and want to increase the temperature by (73.3 - 42) = 31.3 ºC.

The calculation is set up so that all the units cancel, except Joules.

0.466J/gºC 8 (30g)*(31.3ºC) = 437 Joules

Cancel the units of ºC and grams, and we're left with only Joules. It takes 437 Joules to raise 30g of steel 31.3 ºC.

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It is fun to note that the specific heat of water is much higher than steel, or other metals (or even most other materials. - A fact that ET would most certainly have conveyed "Home" if they didn't have any water on his home planet.. Water is 4.186 J/gºC. 30 grams of water requires 3931 Joules to rise 31.3ºC, almost ten times that of steel. Think of this as metals don't like heat, but water loves it. It won't take long for heat to make it's way through a metal pot, but it sure takes the water in it a long time to boil.

Bob

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In doing this calculation, I set the temperature change as (T2 - T1), to gives a positive number, since we are only asked how much is needed. But the proper definition of "temperature change" is (T1-T2), which would make 437 Joules into a negative 437 J, or -437J. This is technically the correct answer. A negative value indicates "heat absorbed." A positive value would mean "heat released." The terms for these two directions are "endothermic" and "exothermic," respectively.