Question #ce46f

1 Answer
Feb 1, 2017

Answer:

#33.3^@"C"#

Explanation:

The key to this problem is the specific heat of olive oil, which is said to be equal to

#c_"olive oil" = "2.19 cal g"^(-1)""^@"C"^(-1)#

As you know, the specific heat of a substance tells you how much heat must be added to #"1 g"# of that substance in order to increase its temperature by #1^@"C"#.

In your case, you must add #"2.19 cal"# of heat for every #"1 g"# of olive oil in order to increase its temperature by #1^@"C"#.

Now, the first thing to do here is to figure out how much heat is needed in order to increase the temperature of #"55.0 g"# of oil by #1^@"C"#

#55.0 color(red)(cancel(color(black)("g"))) * "2.19 cal"/(1color(red)(cancel(color(black)("g"))) * 1^@"C") = "120.45 cal"^@"C"^(-1)#

This means that in order to increase the temperature of #"55.0 g"# of olive oil by #1^@"C"#, you need to supply it with #"120.45 cal"# of heat.

Consequently, adding #"877 cal"# of heat will produce an increase in temperature of

#877 color(red)(cancel(color(black)("cal"))) * overbrace( (1^@"C")/(120.45color(red)(cancel(color(black)("cal")))))^(color(blue)("for 55.0g of olive oil")) = 7.28^@"C"#

Therefore, the final temperature of the olive oil will be

#color(darkgreen)(ul(color(black)(T_"final" = 26.0^@"C" + 7.28^@"C" = 33.3^@"C")))#

The answer is rounded to three sig figs.