The specific heat of aluminum is 0.214 cal/g°c. What is the energy, in calories, necessary to raise the temperature of a 55.5 g piece of aluminum from 23.0 to 48.6°C?

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The specific heat of aluminum is 0.214 cal/g°c. What is the energy, in calories, necessary to raise the temperature of a 55.5 g piece of aluminum from 23.0 to 48.6°C?

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Md Ariful Islam · Answer 1 · Apr 02, 2024 09:48:30

The of aluminium tells you the amount of energy needed to increase the temperature of $"1 g"$ of aluminium by $1^@"C"$.

$c_ "Al" = "0.214 cal g"^(-1)""^@"C"^(-1)$

You can thus say that in order to increase the temperature of $"1 g"$ of aluminium by $1^@"C"$, you need to supply it with $"0.214 cal"$ of heat.

Now, you know that your sample has a mass of $"55.5 g"$. Use the specific heat of aluminium to calculate how much heat would be needed to increase the temperature of this sample

$55.5 color(red)(cancel(color(black)("g"))) * "0.214 cal"/(1color(red)(cancel(color(black)("g"))) * 1^@"C") = "11.877 cal"""^@"C"^(-1)$

So, you now know that in order to increase the temperature of $"5.5 g"$ of aluminium by $1^@"C"$, you need to supply it with $"11.877 cal"$ of heat.

But since you know that the temperature change is equal to

$48.6^@"C" - 23.0^@"C" = 25.6^@"C"$

you can say that you will need

$25.6 color(red)(cancel(color(black)(""^@"C"))) * overbrace("11.877 cal"/(1color(red)(cancel(color(black)(""^@"C")))))^(color(blue)("for 55.5 g of Al")) = color(darkgreen)(ul(color(black)("304 cal")))$

The answer is rounded to three .

The specific heat of aluminum is 0.214 cal/g°c. What is the energy, in calories, necessary to raise the temperature of a 55.5 g piece of aluminum from 23.0 to 48.6°C?

1 Answers