Question

Question #eca79

Answer 1

`"60 K"`

Explanation:

In order to be able to solve this problem, you need to know the specific heat of silver, which is listed as being equal to

`c_"silver" = 0.23"J"/("g K")`

http://www.engineeringtoolbox.com/specific-heat-metals-d_152.html

Now, the idea here is that a substance's specific heat tells you how much energy must be provided in order to increase the temperature of `"1 g"` of that substance by `"1 K"`.

In your case, you know that you provide a `"32-g"` sample of silver with `"300 J"` worth of heat and want to determine how much will the sample's temperature increase.

The equation that establishes a relationship between heat absorbed and change in temperature looks like this

`color(blue)(q = m * c * DeltaT)" "`, where

`q` - the amount of heat absorbed
`m` - the mass of the sample
`c` - the specific heat of the substance
`DeltaT` - the change in temperature, defined as the final temperature minus the initial temperature of the sample.

So, you need to rearrange this equation and solve for `DeltaT`

`q = m * c * DeltaT implies DeltaT = q/(m * c)`

Plug in your values to get

`DeltaT = (300color(red)(cancel(color(black)("J"))))/(32color(red)(cancel(color(black)("g"))) * 0.23color(red)(cancel(color(black)("J")))/(color(red)(cancel(color(black)("g"))) * "K")) = "40.8 K"`

This tells you that the temperature of the sample changed by `"40.8 K"`. Therefore, the final temperature will be

`DeltaT = T_"final" - T_"initial"`

`T_"final" = "40.8 K" + "20 K" = "60.8 K"`

You need to round this off to one sig fig, the number of sig figs you have for the heat absorbed and for the initial temperature

`T_"final" = color(green)("60 K")`