# Help me with my math?

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#### Thoroughbred_Med

##### Full Member
10+ Year Member
So I'm working on a free-standing question in TBR GChem :

"If a 20.0g piece of metal at 75 C with a heat capacity of 0.50 cal/g*K were added to 40g H20 at 25 C, then what would the equilibrium temperature be, assuming no loss of heat to the environment?"

I know how to set up the problem using MCdeltaT water = MCdeltaT metal

so, (40)(1.00)(Tf - 25)K = (20)(0.50)(Tf-75)K

= 40(Tf - 25) = 10(Tf - 75)

= 40Tf - 1000 = 10Tf - 750

= 30Tf = 250

Tf = 8.3 degrees Celcius ... but that's not right

In TBR's answer explanation, they swap the temperature terms in the metal so the math looks like,

(40)(1.00)(Tf - 25)K = (20)(0.50)(75 - Tf)

I always thought deltaT equaled (Tfinal - Tinitial) ??? You get the right answer ( 35 degrees Celsius) if you follow their math but I just don't understand how they can put the Tinitial term first in such an expression?

Can y'all help me out?
Thanks!