Question #769b2

1 Answer
Jul 25, 2017

"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" of water by 1^@"C".

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

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

Now, you're dealing with "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".

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")))