Question #769b2

1 Answer
Jul 25, 2017

"270 J"270 J

Explanation:

The key here is the value of water's specific heat, which, as you know, tells you the amount of heat needed to increase the temperature of "1 g"1 g of water by 1^@"C"1C.

c_"water" = "4.184 J g"^(-1)""^@"C"^(-1)cwater=4.184 J g1C1

You can thus say that in order to increase the temperature of "1 g"1 g of water by 1^@"C"1C, you need to supply it with "4.184 J"4.184 J of heat.

Now, you're dealing with "1.0432 g"1.0432 g of water, so start by calculating the amount of heat needed to increase the temperature of this much water by 1^@"C"1C.

1.0432 color(red)(cancel(color(black)("g"))) * overbrace("4.184 J"/(1color(red)(cancel(color(black)("g"))) * 1^@"C"))^(color(blue)("the specific heat of water")) = "4.365 J"""^@"C"^(-1)

So, you now know that in order to increase the temperature of "1.0432 g" of water by 1^@"C", you need "4.365 J" of heat.

But since you want to increase the temperature of the sample by

88^@"C" - 25.0^@"C" = 63^@"C"

you can say that you will need a total of

63 color(red)(cancel(color(black)(""^@"C"))) * overbrace("4.365 J"/(1color(red)(cancel(color(black)(""^@"C")))))^(color(blue)("for 1.0432 g of water")) = "274.995 J"

Rounded to two sig figs, the number of sig figs you have for the final temperature of the water, the answer will be

color(darkgreen)(ul(color(black)("heat needed = 270 J")))