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)?

Question

Ellie Andrews · Accepted Answer

#"150 cal"#

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.

Jose Ayala · Answer

undefined The heat energy added to the water is 150 calories.