Final temperature for two blocks of iron placed in contact

[dwight_v]

Homework Statement

Two blocks of iron, one of mass m at 10.0C and the other of mass 2m at 25.0c, are placed in contact with each other. If no heat is exchanged with the surroundings, which of the following is the final temperature of the two blocks?
A)10
B)15 .
D) 20C ( this is the answer)

The Attempt at a Solution

I tried to solve doing m(x-10) = 2m(x-25) but then I get x = 40. The answer is 20, but I don't see why you would divide x by 2. [/B]

 

[doggydan42]

What do you think should happen, can you give a range between where you think the final temperature should lie? Should any of the iron blocks lose heat or gain heat?

Use this to think about the signs.

 

[dwight_v]

What do you think should happen, can you give a range between where you think the final temperature should lie? Should any of the iron blocks lose heat or gain heat?

Use this to think about the signs.

ya i think i got it ==> m(x-10) = 2m(25-x) because heat gained = heat lost

 

[gneill]

Moderator's note: Thread title changed to make it more descriptive of the question being asked.

 

[ZapperZ]

ya i think i got it ==> m(x-10) = 2m(25-x) because heat gained = heat lost

I know you figure it out, but I'm going to caution you here because you're making some ad hoc decisions to fit the answer, especially when you reverse the sequence of (25 - x) in your second term.

Follow this rule: ΔT always means T_f - T_i. All you need to do is to write the specific heat equation in just one way:

Q = mc ΔT

In this case, Q = mc(T_f - 10C) + 2mc(T_f - 25C). --- (1)

Now, the simplification here is that (i) Q = 0, since there is no heat loss anywhere, and (ii) c is the same for both. So that equation simplifies to

T_f - 10C + 2T_f - 50C = 0

This gives

3 T_f = 60 C

Thus,

T_f = 20 C.

I did not have to "think" which one loses or gains heat. All I did was set up equation (1), and then I follow the mathematical rule. If I want to know which one gained or lose energy, all I have to do is use the value of T_f that I got, and then look at which of the term in Eq. 1 is positive (heat gained) and which one is negative (heat loss).

The key thing here is that question like this is a TRAP in terms of jumbling up the SIGNS. If you keep the whole equation only to one side of the equation, keeping only "Q" on the other side, you'll never go wrong and you'll never have to insert the sign by hand.

Zz.