Question #d5fe2

1 Answer
Sep 16, 2015

Answer:

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.