The temperature of a sample of water changes from 10° C to 20°C when the sample absorbs 418 joules of heat. What is the mass of the sample?

Question

Avery Adams · Accepted Answer

#"10 g"#

Right from the start, just by inspecting the values given, you can say that the answer will be #"10 g"#.

Here's why that is the case right now.

As you know, a substance's specific heat tells you how much heat is needed to increase the temperature of #"1 g"# of that substance by #1^@"C"#.

Water has a specific heat of approximately #4.18"J"/("g" ""^@"C")#. This tells you that in order to increase the temperature of #"1 g"# of water by #1^@"C"#, you need to provide #"4.18 J"# of heat.

Now, how much heat would be required to increase the temperature of #"1 g"# of water by #10^@"C"#?

Well, you'd need #"4.18 J"# to increase it by #1^@"C"#, another #"4.18 J"# to increase it by another #1^@"C"#, and so on. This means that you'd need

#"4.18 J" xx 10 = "41.8 J"#

to increase the temperature of #"1 g"# of water by #10^@"C"#.

Now look at the value given to you. If you need #"41.8 J"# to increase the temperature of #"1 g"# of water by #10^@"C"#, what mass of water would require #10# times as much heat to increase its temperature by #10^@"C"#?

#"1 g" xx 10 = "10 g"#

That's your response, then.

You can compute this mathematically using the equation

#color(blue)(q = m * c * DeltaT)" "#, where

#q# - heat absorbed/lost #m# - the mass of the sample #c# - the specific heat of the substance #DeltaT# - the change in temperature, defined as final temperature minus initial temperature

Enter your values to obtain

#418 color(red)(cancel(color(black)("J"))) = m * 4.18color(red)(cancel(color(black)("J")))/("g" color(red)(cancel(color(black)(""^@"C")))) * (20 - 10)color(red)(cancel(color(black)(""^@"C")))#

#m = 418/(4.18 * 10) = "10 g"#

Noah Aldrich · Answer

undefined The mass of the sample is 209 grams.