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?

1 Answer
Jun 9, 2017

Answer:

#"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")))#