Specific Heat Capacity Question Mixture Q=MCdeltaT

[dav1d]

Homework Statement

A mixture is made by adding 75g of an unknown liquid at a temperature of 25 degrees Celsius to 60g of water at a temperature of 90 degrees Celsius. The final temperature f the mixture is 65 degrees Celsius. Calculate the specific heat capacity of the liquid. What is the liquid? How are you sure that you are correct?

Homework Equations

Q=m*c*deltaT

The Attempt at a Solution

I don't even know where to start. You can't calculate Q for water because C is not 4.181 at 90 degrees C. You can't find the Q of the unknown liquid because we do not know it's c value...

 

[Ygggdrasil]

You are correct that the heat capacity of a substance (C) varies with temperature. However C does not change very much with temperature, so unless we are doing very precise calculations, we usually just assume stays constant at all temperatures.

 

[dav1d]

Ok, so in that case/

Is it correct to find Q for water with c=4.181, delta T = -25 degrees C

set that equal to mcdeltaT for the unknown liquid, rearrange and solve for c of the unknown and then match it up with a table??

 

[Ygggdrasil]

That sounds like a good plan.

 

[dav1d]

So c, specific heat capacity, changes only slightly between temperatures, so we can assume they are the same always? When does this not work?

 

[Ygggdrasil]

Unless the material changes phase (i.e. liquid water turning into ice or vapor), it's a pretty good assumption that the heat capacity will not change significantly.

 

[Borek]

See for example this table. Specific heat of liquid water between 0°C and 100°C doesn't vary by more than 1%.

Apparently even without phase change differences can be substantial when temperature approaches critical point.

 

[dav1d]

Ok so
Qwater=mcdeltaT
=60g*4.181J/gdegree C*(65-90degree C)
=-6271.5J

Qunknown=6271.5J (flip signs since the energy is absorbed by the unknown liquid)
c=-6271.5J/(75g)(65-25degree C)
=2.0905J/gdegree C

Now I don't know what it is, according to wikipedia tables for specific heat capacity it should be steam? or is it ice? But the question says liquid...

 

[Borek]

Do you have a table with specific heats in your textbook, notes, course materials? If so, look there.

 

[dav1d]

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Do you have a table with specific heats in your textbook, notes, course materials? If so, look there.

I have, but it's pretty much split between ice or steam, which makes no sense since the temperature is too low to form steam and too high to form ice.