Question #d5fe2

1 Answer
Sep 16, 2015

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.