How to Calculate Mass of Aluminum Needed to Melt 20 g of Ice with Heat of Fusion

AI Thread Summary
To determine the mass of aluminum needed to melt 20 g of ice, the heat of fusion for the ice is calculated as Q = (20 g)(79.7 cal/g), resulting in 1594 cal. The next step involves equating this heat to the heat lost by the aluminum using the formula Q = mcdelta T, where the specific heat of aluminum is 0.215 cal/g.C. The challenge lies in finding the final temperature of the aluminum, which is not provided. The discussion suggests that the system will reach thermal equilibrium, indicating that the final temperature will be a steady state between the aluminum and the ice. Understanding the concept of equilibrium is crucial for solving the problem effectively.
dmolson
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Homework Statement


How many grams of aluminum at 90 C would have to be dropped into a hole in a block of ice at 0 C to melt 20 g of ice.


Homework Equations


Q = mcdelta T and Q = mLf
c(H2O) = 1 cal/g.C
c(Al) = 0.215 cal/g.C

The Attempt at a Solution



I can find the heat of fusion Q = (20 g)(79.7 cal/g) = 1594 cal.
The next step I thought would be to set that equal to mcdeltaT of the aluminum, but there is no final temp for the aluminum. I don't know if I am supposed to find the final temp first or how I would do that to find the mass of the aluminum.
 
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dmolson said:
...but there is no final temp for the aluminum.
Only a small portion of the block of ice melts. So what must be the final temperature?
 
Do you know anything about equillibrium? It could be easily shown that this system would reach steady state right?
 
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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