Question

Question #769b2

Answer 1

`"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")))`