Question #509d0

2 Answers
Mar 24, 2017

Answer:

The heat required, #Q#, is #"4630 J"#.

Explanation:

Use the following equation:

#Q=mcDeltaT#,

where #Q# is the amount of heat energy, #m# is mass, #c# is specific heat capacity, #DeltaT#. #DeltaT=T_"final"-T_"initial"#

Given
#m="66.7"#
#c="0.75 J/(g"^@"C")#
#DeltaT="92.5"^@"C"-0.0^@"C"=92.5^@"C"#

Unknown: #Q#

Solution
Substitute the given values into the equation and solve.

#Q=(66.7color(red)cancel(color(black)("g")))xx((0.75color(white)(.)"J")/(color(red)cancel(color(black)("g"^@"C"))))xx(92.5color(red)cancel(color(black)(""^@"C")))="4630 J"#

(rounded to three significant figures)

Mar 24, 2017

Answer:

#"4630 J"#

Explanation:

Here's an alternative approach that you can use to double-check your calculations.

As you know, a substance's specific heat tells you the amount of heat needed to increase the temperature of #"1 g"# of said substance by #1^@"C"#.

In your case, you know that silicon carbide has a specific heat of

#c_"SiC" = "0.75 J g"^(-1)""^@"C"^(-1)#

This tells you that in order to increase the temperature of #"1 g"# of silicon carbide by #1^@"C"#, you must provide it with #"0.75 J"# of energy.

Now, you can use the specific heat as a conversion factor to help you determine the amount if heat needed to increase the temperature of #"66.7 g"# of silicon carbide by #1^@"C"#

#66.7 color(red)(cancel(color(black)("g"))) * "0.75 J"/(1color(red)(cancel(color(black)("g"))) * 1^@"C") = "50.025 J"""^@"C"^(-1)#

Now that you know how much heat will increase the temperature of #"66.7 g"# of silicon carbide by #1^@"C"#, you can use this as a conversion factor to find the heat needed to increase the temperature of the sample by

#92.5^@"C" - 0.0^@"C" = 92.5^@"C"#

You should end up with

#92.5 color(red)(cancel(color(black)(""^@"C"))) * overbrace("50.025 J"/(1color(red)(cancel(color(black)(""^@"C")))))^(color(blue)("for 66.7 g SiC")) = color(darkgreen)(ul(color(black)("4630 J")))#

The answer is rounded to three sig figs.