# 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?

May 18, 2017

T_f ~~ 20°C

#### Explanation:

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

$q = m c \Delta T$

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
$\Delta T = {T}_{f} - {T}_{i}$
and ${T}_{f} - {T}_{i} =$ final temperature minus initial temperature

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

${T}_{f} = \frac{q}{m c} + {T}_{i}$

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