# Question #4719e

##### 1 Answer

#### Explanation:

Your tool of choice here will be this equation

#color(blue)(ul(color(black)(q = m * c * DeltaT)))#

Here

#q# is the heat lost or gained by the substance#m# is themassof the sample#c# is thespecific heatof the substance#DeltaT# is thechange in temperature, defined as the difference between thefinal temperatureand theinitial temperatureof the sample

As you know, the specific heat of copper is listed as

#c_"copper" = "0.385 J g"^(-1)""^@"C"^(-1)#

http://www2.ucdsb.on.ca/tiss/stretton/database/specific_heat_capacity_table.html

So, the problem wants you to determine the mass of copper that would undergo a

The temperature of the sample *increases* by

#DeltaT = 35.5^@"C"#

Rearrange the equation to isolate

#q = m * c * DeltaT implies m = q/(c * DeltaT)#

Plug in your values to find

#m = (943.06 color(red)(cancel(color(black)("J"))))/(0.385 color(red)(cancel(color(black)("J"))) "g"^(-1) color(red)(cancel(color(black)(""^@"C"^(-1)))) * 35.5 color(red)(cancel(color(black)(""^@"C")))) = color(darkgreen)(ul(color(black)("69.0 g")))#

The answer is rounded to three **sig figs**.

This means that if you supply

**ALTERNATIVE APPROACH**

You can get the same result by using the *specific heat* of the metal, which tells you that in order to increase the temperature of

Start by calculating the amount of energy needed to increase the temperature of

#35.5 color(red)(cancel(color(black)(""^@"C"))) * "0.385 J"/("1 g" * 1color(red)(cancel(color(black)(""^@"C")))) = "13.6675 J g"^(-1)#

Since you know that you have

#943.06 color(red)(cancel(color(black)("J"))) * overbrace("1 g"/(13.6675color(red)(cancel(color(black)("J")))))^(color(blue)("needed for 35.5"^@"C increase in temperature")) = color(darkgreen)(ul(color(black)("69.0 g")))#