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?

1 Answer
Eidola
May 18, 2017

#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#

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