What is the specific heat of the metal?

AI Thread Summary
The discussion revolves around calculating the specific heat of a metal using a heat transfer equation involving a metal container, water, and a piece of metal at a high temperature. The user is struggling with the calculation despite using the correct equation, which includes the specific heat of water. Participants suggest ensuring that the mass is converted to grams and confirm that the specific heat of water is approximately 4.2 J/g°C. There is a request for the user to detail their calculation steps to identify potential errors. The conversation emphasizes the importance of unit consistency in thermal calculations.
hatingphysics
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A metal container, which has a mass of 9.0 kg contains 17.6 kg of water. A 2.0-kg piece of the same metal, initially at a temperature of 200.0°C, is dropped into the water. The container and the water initially have a temperature of 15.1°C and the final temperature of the entire system is 17.1°C. Calculate the specific heat of the metal.

I used this equation but I still can't seem to get the right answer...[C(metal)*Mass(container)*deltaT(container)] + [4186*Mass(water)*deltaT(water)] = Cmetal*Mass(peice)*deltaT(piece)

HELP PLEASE!:confused:
 
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Your equation seems correct. Just make sure your mass is in grams and that the specific heat of water that you use is about 4.2 (I noticed you forgot to put a decimal there...or was that a typo?).

If you write out your steps you took, maybe one of us can help determine where your error lies.
 
it's not a typo. He did not present us with his units. This is the specific heat of water in J/kg.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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