Question

Question #d5fe2

Answer 1

You need `"10,000 J"` worth of heat.

Explanation:

Start by taking a look at sand's specific heat, which is said to be equal to `664"J"/("kg" ^@"C")`.

When given in Joules per kilogram Kelvin, the specific heat of a substance tells you how much heat is required to increase the temperature of `"1 kg"` of that substance by `1^@"C"`.

In your case, if you add `"664 J"` to `"1 kg"` of sand, you will increase its temperature by `1^@"C"`.

Since you need to increase its temperature by `20^@"C"`, it follows that you must supply 20 times more heat than you would have supplied to increase the temperature by only `1^@"C"`.

The equation that links added/removed heat to increase/decrease in temperature looks like this

`q = m * c * DeltaT" "`, where

`q` - the amount of heat;
`m` - the mass of the sample;
`c` - the specific heat of the sample;
`DeltaT` - the change in temperature, defined as the difference between the final temperature and the initial temperature of the sample.

So, use the value given to yout to find

`q = 1color(red)(cancel(color(black)("kg"))) * 664"J"/(color(red)(cancel(color(black)("kg"))) * color(red)(cancel(color(black)(""^@"C")))) * (50-30)color(red)(cancel(color(black)(""^@"C")))`

`q = "13,280 J" = color(green)("10,000 J")`

The answer is rounded to one sig fig, the number of sig figs you gave for the mass of the sample.