# needing help isolating the variable Ch

#### mathnubb

##### New member
I'm not terribly good with algebra, and I need to isolate a variable in the following equation:

1 2 3
Mh x Ch x DeltaTh = Mc x Cc x DeltaTc

I need to isolate the varible Ch, and I can't seem to do it properly. Could somebody kindly give me a hand? Thank you!
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Edited by stapel -- Reason for edit: "language", punctuation, etc

#### stapel

##### Super Moderator
Staff member
What do the "1 2 3" digits have to do with the equation in the next line? You say that "Ch" is a variable, but usually C and h would be separate variables, which leads to questions regarding what the others might might. For instance, is "DeltaTc" one variable (perhaps "$$\displaystyle \Delta(Tc)$$"), two, or three? Why is the variable "x" scattered throughout, rather than gathered together?

Eliz.

#### mathnubb

##### New member
This is a physics/chemistry question. Sorry; I'll try to explain it more clearly this time. The variables are defined like this:

. . .Mh: mass of hot metal
. . .Ch: heat capacity of hot metal
. . .DeltaTh: Change in temperature of Hot metal
. . .Mc: mass of cold water
. . .Cc: heat capacity of water
. . .DeltaTc: Change in temperature of Cold water

The "c" and "h" are just subscripts. The x's indicate multiplication.

I'm trying to isolate "Ch". When substituting values for the variables, I'm not ending up with a heat capacity anywhere near what I think the answer ought to be.

Using that equation above, I change the DeltaT's to "Tfc - Tic" and "Tfh - Tih", but since "Tf" for both the water and the metal are the same, the two can just be called "Tf". Then I make this long eqaution:

. . .MhChTf - MhChTih = McCcTf - McCcTic

The common factor is Ch; this is where I get lost.

. . .Ch(MhTf - MhTih) = McCcTf - McCcTic
. . .Ch = (McCcTf - McCcTic) / (MhTf - MhTih)

Then i would subststite values in to find Ch, but it always comes out negative. Any advice?

#### stapel

##### Super Moderator
Staff member
So the equation is as follows...?

. . . . .M<sub>h</sub> C<sub>h</sub> delta-T<sub>h</sub> = M<sub>c</sub> C<sub>c</sub> delta-T<sub>c</sub>

And you're wanting to solve for C<sub>h</sub>...?

Since all that's been done is multiplication, just divide off the other two factors:

. . . . .$$\displaystyle \L C_h\, =\, \frac{M_c C_c \Delta T_c}{M_h \Delta T_h}$$

Since we don't have the chemico-physical information (numerical values, chemical relationships, etc), we cannot speak to the answer(s) you are obtaining. Sorry.

Eliz.

#### mathnubb

##### New member
thank you man, it was actually easier than i did it lol, i always always overlook things