Question #eca79

1 Answer
Nov 8, 2015

Answer:

#"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")#