Question #c1168

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Question #c1168

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Answer 1 · 2017-03-18T02:50:06

$2464 J$ $"2464 J"$

Explanation:

The key to this problem is the specific heat of the metal.

You know that copper has a specific heat of

$c_{copper} = {0.3850 J g}^{- 1}^{\circ} C^{- 1}$ $c_"copper" = "0.3850 J g"^(-1)""^@"C"^(-1)$

This tells you that in order to increase the temperature of $1 g$ $"1 g"$ of copper by $1^{\circ} C$ $1^@"C"$ , you need to provide it with $0.3850 J$ $"0.3850 J"$ of heat.

Now, how much energy would be needed in order to increase the temperature of $715.0 g$ $"715.0 g"$ of copper by just $1^{\circ} C$ $1^@"C"$ ? Use the specific heat as a conversion factor to get

$715.0 color(red)(cancel(color(black)("g"))) * overbrace("0.3850 J"/(1color(red)(cancel(color(black)("g"))) * 1^@"C"))^(color(blue)("the specific heat of copper")) = "275.275 J"^@"C"^(-1)$

Since you know that you need $"275.275 J"$ of heat in order to increase the temperature of $"715.0 g"$ of copper by $1^@"C"$ , you can say that in order to increase its temperature by

$22.46^@"C" - 13.51^@"C" = 8.95^@"C"$

you will need to provide

$8.95 color(red)(cancel(color(black)(""^@"C"))) * "275.275 J"/(1color(red)(cancel(color(black)(""^@"C")))) = color(darkgreen)(ul(color(black)("2464 J")))$

The answer is rounded to four sig figs.

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Question #c1168

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