Question

Question #897e7

Answer 1

`360.^@"C"`

Explanation:

You can't answer this question without knowing the specific heat of iron

`c_"iron" = "0.45 J g"^(-1)""^@"C"^(-1)`

http://www.engineeringtoolbox.com/specific-heat-metals-d_152.html

Now, the specific heat of a substance tells you the amount of heat needed to increase the temperature of `"1 g"` of that substance by `1^@"C"`.

In your case, the specific heat of iron tells you that in order to increase the temperature of `"1 g"` of iron by `1^@"C"`, you need to provide it with `"0.45 J"` of heat.

Use this value to determine the amount of heat needed to increase the temperature of `"445 g"` of iron by `1^@"C"`

`445 color(red)(cancel(color(black)("g"))) * "0.45 J"/(1color(red)(cancel(color(black)("g"))) * 1^@"C") = "200.25 J"^@"C"^(-1)`

So, you now know that if you add `"200.25 J"` of heat to `'445 g"` of iron, you will increase its temperature by `1^@"C"`.

This implies that `"65,100 J"` of heat will increase the temperature of `"445 g"` of iron by

`"65,100" color(red)(cancel(color(black)("J"))) * overbrace( (1^@"C")/(200.25color(red)(cancel(color(black)("J")))))^(color(blue)("for 445 g of iron")) = 325^@"C"`

Therefore, the final temperature of the piece of iron will be

`color(darkgreen)(ul(color(black)("final temperature" = 35.0^@"C" + 325^@"C" = 360.^@"C")))`

The answer is rounded to three sig figs, no decimal places.