Question

The same heat transfer into identical masses of different substances produces different temperature changes. Calculate the final temperature when 1.00 kcal of heat transfers into 1.00 kg of the following, originally at $20.0^\circ\textrm{C}$: (a) water; (b) concrete; (c) steel; and (d) mercury.

- $21.0^\circ\textrm{C}$
- $25.0^\circ\textrm{C}$
- $29.3^\circ\textrm{C}$
- $50.1^\circ\textrm{C}$

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This is College Physics Answers with Shaun Dychko. We are going to figure out the final temperature of four different substances given that they each get 1 kilocalorie of heat; they have a mass of 1.00 kilogram and an initial temperature of 20.0 degrees Celsius. We are going to change our units of heat energy into joules by multiplying by 4186 joules for every kilocalorie. Now we know that the amount of heat transferred is the mass times the specific heat times the change in temperature and the change in the temperature is the final temperature minus the initial temperature. And we can solve this for

*T f*by first dividing both sides by*mc*, switching the sides around and then add initial temperature to both sides and we get that the final temperature is the initial temperature plus the heat energy divided by the mass times the specific heat of the material. So in part (a) we are dealing with water so the final temperature is 20.0 degrees Celsius plus 4186 joules divided by 1.00 kilogram times the specific heat of water which we have to look up in this table [14.1] (and... where's water...) water has a specific heat of 4186 joules per kilogram per Celsius degree and this is water at 15.0 degrees Celsius— we'll assume that this specific heat is pretty much the same at 20.0; this specific heat doesn't change that much for solids and liquids— so the final temperature will be 21.0 degrees Celsius. In part (b), we have concrete and all the numbers are the same as it was for water except the specific heat now for concrete— we have to look up— and that is 840 joules per kilogram per Celsius degree so it has a lower specific heat. So its temperature will change more for a given amount of energy and sure enough its final temperature is 25.0 degrees Celsius. Steel has a specific heat of 452 joules per kilogram per Celsius degree and we plug that number in for*c*here and all the other things being the same, we end up with 29.3 degrees Celsius. And mercury has a specific heat of 139 and a final temperature of 50.1 degrees Celsius.