# Question #b29dc

##### 1 Answer

#### Explanation:

The key to understanding this type of problems lies with the substance's specific heat.

For a given substance, its **specific heat** will tell you how much heat is needed in order to increase the mass of

In your case, the specific heat of gold is said to be

#c = 0.128"J"/("g" ""^@"C")#

This tells you that you need **for every** gram of the sample **and for every**

So, for example, your sample of gold is said to have a mass of **just**

Well, since you need **for every gram**, and since you only want to increase its temperature by

#20 xx "0.128 J" = "2.56 J"#

But you ended up using **went into increasing the sample's temperature!**

You can say that

#x xx "2.56 J" = "96 J"#

Here **increase in temperature** produced by adding that extra heat to the sample. This means that you have

#x = 96/2.56 = 37.5#

The temperature of the coin increased by

You actually have an equation that you can use for such problems

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

*change in temperature*

Plugging your values into this equation will once again give you

#DeltaT = q/(m * c)#

#DeltaT = (96 color(red)(cancel(color(black)("J"))))/(20 color(red)(cancel(color(black)("g"))) * 0.128color(red)(cancel(color(black)("J")))/(color(red)(cancel(color(black)("g"))) ""^@"C")) = 37.5^@"C"#

I'll leave the answer rounded to two sig figs

#DeltaT = color(green)(38^@"C")#