WEBVTT

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This is Giancoli Answers
with Mr. Dychko.

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The heat lost
by this mystery substance

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has been equal the heat gained
by this calorimeter cup

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and the water that it contains

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and also the glass thermometer
that's inside of it.

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So, all of these things
will be in equilibrium

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when the total heat lost
by the substance

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equals the total heat gained
by everything else.

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So, we have mass of aluminium
times specific heat of aluminium

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times the change in temperature
of the calorimeter

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plus mass of water
times specific heat of water

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times the same change in temperature

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because the calorimeter,
the water and the glass thermometer

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all start at the same temperature

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and they all have the same final temperature.

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So, they have
the same change in temperature

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let's call it <i>ΔTc</i>

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for a change of temperature of the
calorimeter and everything that's in it.

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Plus the mass of the glass
times specific heat of glass

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times its change in temperature.

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So, a factor out the <i>ΔTc</i>
and you get this line here,

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and then divide both sides by <i>ms</i>

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and change in temperature
of this mystery substance

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and we can solve
for the specific heat of this substance.

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So, it's changing temperature

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times all this stuff
divided by mass of the substance

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times the initial temperature
of the substance

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minus its final temperature.

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And we have initial minus final
whenever we have heat lost.

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So, that's 35 degrees Celsius
minus 10.5 degrees Celsius,

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and that's final temperature
minus the initial temperature

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for the calorimeter
and everything that was initially inside it.

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Times 0.105 kilograms mass
of the calorimeter

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times 900 joules
per kilogram Celsius degree,

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specific heat of aluminum

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plus 0.185 kilograms,
mass of the water,

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times 4,186 joules
per kilogram Celsius degree,

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specific heat of water.

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I'm not writing all the unit's here

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because there's so many
numbers and units

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that it would take a long time to write.

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Plus 0.017 kilograms
for the mass of the glass

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that thermometer’s made out of

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plus it or times 840
joules per kilogram Celsius degrees,

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specific heat of glass,

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divided by 0.21 of kilograms mass
of this mystery substance

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times its initial temperature
of 333 degrees Celsius

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minus this final temperature
of 35 degrees Celsius.

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And so a specific heat must be 341
joules per kilogram Celsius degree.