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An ancient copper coin was found to absorb 545.8 J of heat when the temperature increases 31.4 C°. The specific heat of copper is 0.387 J/g°C. What is the mass of the copper coin?

Answer 1

Caleb Adams

The mass of the copper coin is 44.9 g.

The formula for the heat absorbed by a substance is

#color(blue)(|bar(ul(color(white)(a/a) q = mcΔT color(white)(a/a)|)))" "#

where

#q# is the quantity of heat

#m# is the mass of the substance

#c# is the specific heat capacity of the material

#ΔT# is the temperature change

You can rearrange the formula to calculate the specific heat capacity:

#m = q/(cΔT)#

#m = (545.8 color(red)(cancel(color(black)("J"))))/(0.387 color(red)(cancel(color(black)("J·°C"^"-1")))"g"^"-1" × 31.40 color(red)(cancel(color(black)("°C")))) = "44.9 g"#

Wouldn't it have been easier to weigh the coin on a balance?

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Answer 2

Mateo Aguilar

Use the formula: ( Q = mc\Delta T ) Rearrange for mass: ( m = \frac{Q}{c\Delta T} ) Substitute values: ( m = \frac{545.8 , J}{(0.387 , J/g°C)(31.4 , °C)} ) Calculate: ( m \approx 44.2 , g )

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.