Question

Question #509d0

Answer 1

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)

Answer 2

`"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.