Question

How many joules are required to heat 15.2 g of water at 35.0°C to 70.0°C?

Answer 1

`"2,220 J"`

Explanation:

In order to be able to determine how much heat is required to increase the temperature of your sample of water from `35.0^@"C"` to `70.0^@"C"`, you need to know the value of water's specific heat.

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

Water has a specific heat of about `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 it with `"4.18 J"` of heat.

Now, here's how you can think about what's going on here. in order to increase the temperature of `"4.18 g"` of water by `1^@"C"`, you would need `4.18` times more heat than water's specific heat value.

Likewise, in order to increase the temperature of `"4.18 g"` of water by `4.18^@"C"`, you'd need `(4.18 xx 4.18)` times more heat than water's specific heat value.

In your case, you need to increase the temperature of `"15.2 g"` of water by `35.0^@"C"`, which tells you that you're going to need `(15.2 xx 35)` times more heat than water's specific heat value.

Mathematically, this is expressed as

`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

`q = 15.2 color(red)(cancel(color(black)("g"))) * 4.18"J"/(color(red)(cancel(color(black)("g"))) color(red)(cancel(color(black)(""^@"C")))) * (70.0 - 35.0)color(red)(cancel(color(black)(""^@"C")))`

`q = "2223.76 J"`

Rounded to three sig figs, the answer will be

`q = color(green)("2,220 J")`