Question

A 10.0 g sample of pure gold (Au) at 55.0 C gives off 45.0 J of heat to its surroundings. The specific heat capacity (C) of Au is 0.129J/g*C. What is the final temperature, in C, of the Au sample?

Answer 1

`T_f ~~ 20°C`

Explanation:

The equation you're going to want to use here is:

`q = mcDeltaT`

In this equation, the parameters are defined as follows:

`q =` energy gained or lost by the system (in this case, the gold)
`m =` mass
`c =` specific heat capacity
`DeltaT = T_f - T_i`
and `T_f - T_i =` final temperature minus initial temperature

Now rearrange the equation to solve for final temperature...

`T_f = q/(mc) + T_i`

And simply plug in your given parameters from the problem. Note that `q` should be negative because the problem states that the gold loses heat.

`T_f = (-45.0J)/(10.0g*(0.129 J/(g*°C))) + 55°C`

Cancel units, if it's easier to think of that way.

`T_f = (-45.0cancel(J))/(10.0cancelg*(0.129 cancel(J)/(cancelg*°C))) + 55°C`

Do the math...

`T_f ~~ 20°C`