# A 15.75-g piece of iron absorbs 1086.75 joules of heat energy, and its temperature changes from 25°C to 175°C. What is the specific heat capacity of iron?

##### 1 Answer

#### Answer:

#### Explanation:

Your task here is to find the specific heat of iron, so take a second to make sure that you understand what it is you're looking for.

A substance's **specific heat** tells you how much heat is needed in order to increase the temperature of

So, in essence, you're looking for amount of heat **per unit of mass** and **per unit of temperature**.

#color(blue)("specific heat" = "heat"/("unit of mass " xx " unit of temperature"))#

Now, let's assume that you **don't know** the equation that establishes a relationship between heat added, the mass of the sample, the specific heat of the substance, and the resulting increase in temperature.

Here's how you could play around with the information provided by the problem to understand how to find the specific heat of iron.

*Scenario 1*

For instance, let's assume that adding **per gram** of iron will be

#"1086.75 J"/"15.75 g" = "69 J/g"#

In this scenario, adding **for every** gram of iron will increase its temperature by

*Scenario 2*

Now let's assume that this much heat would increase the temperature of

#DeltaT = 175^@"C" - 25^@"C" = 150^@"C"#

In this case, the amount of heat needed **per degree Celsius** will be

#"1086.75 J"/(150^@"C") = "7.245 J/"""^@"C"#

In this scenario, you will get a **for every**

*In real life*

But since you know that adding that much heat will increase the temperature of

#"1086.75 J"/("15.75 g" * 150^@"C") = 0.46"J"/("g" ""^@"C")#

And this is the substance's **specific heat**. So, to find the specific heat of a substance, you need to divide the amount of heat used to produce that increase in temperature for the given sample.

The equation that you'll be using from now on looks like this

#color(blue)(q = m * c * DeltaT)" "# , where