# How much heat is given off when a 24.7 kg iron ingot is cooled from 880°C to 13°C?

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The specific heat of iron is 0.107 cal/g * °C.

The specific heat of iron is 0.107 cal/g * °C.

##### 1 Answer

#### Explanation:

Notice that the problem provides you with the mass of the iron ingot, but that it's being expressed in *kilograms*.

Since the **specific heat** of iron is given in *joules per gram Celsius*, *kilograms* to *grams* before doing anything else

#24.7 color(red)(cancel(color(black)("kg"))) * (10^3"g")/(1color(red)(cancel(color(black)("kg")))) = 24.7 * 10^3"g"#

Now, you can use the specific heat of iron to figure out how much heat would be **released** when the temperature of

#24.7 * 10^3 color(red)(cancel(color(black)("g"))) * overbrace("0.107 cal"/(1color(red)(cancel(color(black)("g"))) ""^@"C"))^(color(purple)("the specific heat of iron")) = 2.643 * 10^3"cal" ""^@"C"^(-1)#

This tells you that in order to cause a

In your case, the temperature of the ingot must decrease by

#"change in temperature" = |13^@"C" - 880^@"C"| = 867^@"C"#

You can thus say that when the temperature of

#867 color(red)(cancel(color(black)(""^@"C"))) * overbrace((2.643 * 10^3"cal")/(1color(red)(cancel(color(black)(""^@"C")))))^(color(purple)("for 2.643" * 10^3"g of iron")) = color(green)(bar(ul(|color(white)(a/a)color(black)(2.3 * 10^6"cal")color(white)(a/a)|)))#

The answer is rounded to two **sig figs**.