Question

A piece of gold initially at a temperature of 25.1 °C absorbs 675 J of heat, raising its temperature to 57.4 °C. Assuming the specific heat of gold is 0.126 J/(g°C), what is the mass of the sample?

Answer 1

`"166 g"`

Explanation:

The key here is the specific heat of gold, which is said to be equal to

`c_"gold" = "0.126 J g"^(-1)""^@"C"^(-1)`

This tells you that in order to increase the temperature of `"1 g"` of gold by `1^@"C"`, you need to provide it with `"0.126 J"` of heat.

In your case, the temperature increases from `25.1^@"C"` to `57.4^@"C"`, which implies that it changes by

`57.4^@"C" - 25.1^@"C" = 32.3^@"C"`

Now, you can use the specific heat of gold to calculate how much energy would be needed to increase the temperature of gold by `32.3^@"C"`.

`32.3 color(red)(cancel(color(black)(""^@"C"))) * "0.126 J"/("1 g" * 1color(red)(cancel(color(black)(""^@"C")))) = "4.0698 J g"^(-1)`

This tells you that in order to increase the temperature of `"1 g"` of gold by `32.3^@"C"`, you need to provide it with `"4.0698 J"` of heat.

You can thus say that `"675 J"` of heat will increase the temperature of

`675 color(red)(cancel(color(black)("J"))) * "1 g"/(4.0698color(red)(cancel(color(black)("J")))) = "165.86 g"`

of gold by `32.3^@"C"`. Rounded to three sig figs, the answer will be

`color(darkgreen)(ul(color(black)("mass of gold = 166 g")))`