Question

How do you determine the mass of a water sample that is heated from an initial temperature of 25 deg C to a final temperature of 100 deg C following the addition of 1200 J of heat energy?

Answer 1

Here's how I would do it.

Explanation:

The formula for the amount of heat absorbed by a substance is

`color(blue)(bar(ul(|color(white)(a/a)q = mcΔTcolor(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 mass:

`m = q/(cΔT)`

In your problem,

`q = "1200 J"`

`c = "4.184 J·°C"^"-1""g"^"-1"` (the specific heat capacity of water)

`ΔT = T_f - T_i = "100 °C - 25 °C" = "75 °C"`

∴ `m = (1200 color(red)(cancel(color(black)("J"))))/(4.184 color(red)(cancel(color(black)("J·°C"^"-1")))"g"^"-1" × 75 color(red)(cancel(color(black)("°C")))) = "3.8 g"`