To what temperature will a 50.0 g piece of glass raise if it absorbs 5275 joules of heat and its specific heat capacity is 0.50 J/g°C, if the initial temperature of the glass is 20.0°C?

1 Answer
Jan 29, 2016

Answer:

#230^@"C"#

Explanation:

A substance's specific heat tells you how much heat much either be added or removed from #"1 g"# of that substance in order to cause a #1^@"C"# change in temperature.

The change in temperature, #DeltaT#, is always calculated by subtracting the initial temperature of the sample from the final temperature of the sample.

#color(blue)(DeltaT = T_"final" - T_"initial")#

Now, when the substance absorbs heat, its temperature will increase, which implies that #DeltaT > 0#.

Your goal here will be to find the change in temperature first, then use it to find the final temperature of the sample.

You will have to use this equation

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

#q# - the amount of heat added / removed
#m# - the mass of the sample
#c# - the specific heat of the substance
#DeltaT# - the change in temperature

As you can see, this equation establishes a relationship between the amount of heat added or removed from a sample, the mass of that substance, its specific heat, and the resulting change in temperature.

In your case, adding #"5275 J"# of heat to that #"50.0-g"# piece of glass will result in a temperature change of

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

Plug in your values to get

#DeltaT = (5275 color(red)(cancel(color(black)("J"))))/(50.0color(red)(cancel(color(black)("g"))) * 0.50color(red)(cancel(color(black)("J")))/(color(red)(cancel(color(black)("g"))) ""^@"C")) = 211^@"C"#

So, adding that much heat to your sample will result in a #211^@"C"# increase in temperature. This means that the final temperature of the glass will be

#T_"final" = T_"initial" + DeltaT#

#T_"final" = 20.0^@"C" + 211^@"C" = color(green)(230^@"C")#

The answer is rounded to two sig figs, the number of sig figs you have for the specific heat of glass.