What is the initial temperature of the heated aluminum bolt?

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The discussion centers on calculating the initial temperature of a heated aluminum bolt placed in water and a copper calorimeter. The user initially used the wrong formula, leading to an incorrect result of 541.3 degrees Celsius. Key points include the need to account for all three masses in the heat transfer equation and the importance of correctly expressing heat loss and gain in terms of temperature. Participants emphasize the necessity of careful attention to the signs of temperature changes. The conversation highlights the complexities of calorimetry problems and the importance of thorough calculations.
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An aluminum bolt has a mass of 21.3 g. It is heated then placed into 839 g of water in a copper calorimeter cup with a mass of 137 g. The initial temperature of the water and the copper cup is 16 oC. The bolt, water and cup arive at an equilibrium temperature of 18.4 oC. What was the temperature in degrees celcius of the bolt before it was placed in the water?
 
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I used this formula and got wrong answer, need help.

Tf = (m1C1T1 + m2C2T2) / (m1C1 + m2C2)

And got 541.3 Degrees C. What is wrong.?
 
I see three masses in the problem statement and you only have two in your equation...
 
It's never a good idea to write a one line answer, because this will usually give incorrect results. First observe that the heat (heat, not temperature) lost by the bolt is equal to the heat gained by the calorimeter and the water. Figure out how to express the heat loss and the heat gain in terms of temperature. Pay careful attention to the sign of your delta T's. And then finally, solve for the desired quantity.
 
sounds like homework to me.
 
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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