Question #897e7

1 Answer
May 30, 2017

Answer:

#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.