Question #769b2

1 Answer
Jul 25, 2017

Answer:

#"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")))#