Question

The temperature of a sample of water changes from 10° C to 20°C when the sample absorbs 418 joules of heat. What is the mass of the sample?

Answer 1

`"10 g"`

Explanation:

Right from the start, just by inspecting the values given, you can say that the answer will be `"10 g"`.

Now, here's what that is the case.

As you know, a substance's specific heat tells you how much heat is needed to increase the temperature of `"1 g"` of that substance by `1^@"C"`.

Water has a specific heat of approximately `4.18"J"/("g" ""^@"C")`. This tells you that in order to increase the temperature of `"1 g"` of water by `1^@"C"`, you need to provide `"4.18 J"` of heat.

Now, how much heat would be required to increase the temperature of `"1 g"` of water by `10^@"C"`?

Well, you'd need `"4.18 J"` to increase it by `1^@"C"`, another `"4.18 J"` to increase it by another `1^@"C"`, and so on. This means that you'd need

`"4.18 J" xx 10 = "41.8 J"`

to increase the temperature of `"1 g"` of water by `10^@"C"`.

Now look at the value given to you. If you need `"41.8 J"` to increase the temperature of `"1 g"` of water by `10^@"C"`, what mass of water would require `10` times as much heat to increase its temperature by `10^@"C"`?

`"1 g" xx 10 = "10 g"`

And that's your answer.

Mathematically, you can calculate this by using the equation

`color(blue)(q = m * c * DeltaT)" "`, where

`q` - heat absorbed/lost
`m` - the mass of the sample
`c` - the specific heat of the substance
`DeltaT` - the change in temperature, defined as final temperature minus initial temperature

Plug in your values to get

`418 color(red)(cancel(color(black)("J"))) = m * 4.18color(red)(cancel(color(black)("J")))/("g" color(red)(cancel(color(black)(""^@"C")))) * (20 - 10)color(red)(cancel(color(black)(""^@"C")))`

`m = 418/(4.18 * 10) = "10 g"`