Question

A calorimeter contains 15 grams of water. The water's temperature increases by 10 C°. How much heat energy was added to the water? (Hint: water's specific heat is 1 cal/g°C)?

Answer 1

`"150 cal"`

Explanation:

Unsurprisingly, the key to this problem is the hint.

The thing to remember about a substance's specific heat is that it tells you the amount of energy needed in order increase the temperature of `"1 g"` of said substance by `1^@"C"`.

Now, water is said to have a specific heat of `"1 cal g"^(-1)""^@"C"^(-1)`. This tells you that in order to increase the temperature of `"1 g"` of water by `1^@"C"`, you must provide it with `"1 cal"` of heat.

The thing to remember here is that you need `"1 cal"` of heat for every `"1 g"` of water and for every `1^@"C"` in temperature.

So, you have `"15 g"` of water to work with. You can use the specific heat of water to figure out how much heat is needed to increase the temperature of this sample by `1^@"C"`.

`15 color(red)(cancel(color(black)("g"))) * "1 cal"/(1color(red)(cancel(color(black)("g"))) * 1^@"C") = "15 cal" ""^@"C"^(-1)`

This tells you that for every `1^@"C"` increase in the temperature of the sample, `"15 cal"` of heat are needed. Since you want the temperature to increase by `10^@"C"`, you will need

`10color(red)(cancel(color(black)(""^@"C"))) * overbrace("15 cal"/(1color(red)(cancel(color(black)(""^@"C")))))^(color(blue)("for 15 g of water")) = color(darkgreen)(ul(color(black)("150 cal")))`

I'll leave the answer rounded to two sig ifgs, but keep in mind that you only have one significant figure for the increase in temperature.