A piece of gold initially at a temperature of 25.1 °C absorbs 675 J of heat, raising its temperature to 57.4 °C. Assuming the specific heat of gold is 0.126 J/(g°C), what is the mass of the sample?

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

The key here is the of gold, which is said to be equal to

$c_"gold" = "0.126 J g"^(-1)""^@"C"^(-1)$

This tells you that in order to increase the temperature of $"1 g"$ of gold by $1^@"C"$, you need to provide it with $"0.126 J"$ of heat.

In your case, the temperature increases from $25.1^@"C"$ to $57.4^@"C"$, which implies that it changes by

$57.4^@"C" - 25.1^@"C" = 32.3^@"C"$

Now, you can use the specific heat of gold to calculate how much energy would be needed to increase the temperature of gold by $32.3^@"C"$.

$32.3 color(red)(cancel(color(black)(""^@"C"))) * "0.126 J"/("1 g" * 1color(red)(cancel(color(black)(""^@"C")))) = "4.0698 J g"^(-1)$

This tells you that in order to increase the temperature of $"1 g"$ of gold by $32.3^@"C"$, you need to provide it with $"4.0698 J"$ of heat.

You can thus say that $"675 J"$ of heat will increase the temperature of

$675 color(red)(cancel(color(black)("J"))) * "1 g"/(4.0698color(red)(cancel(color(black)("J")))) = "165.86 g"$

of gold by $32.3^@"C"$. Rounded to three , the answer will be

$color(darkgreen)(ul(color(black)("mass of gold = 166 g")))$

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