What Phases are Present at Equilibrium in a Water and Ice Mixture?

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In a mixture of water and ice in an insulated container, the equilibrium phase depends on the heat transfer between the two. The heat absorbed by the ice to reach its melting point is 400 J, and the total heat needed for it to melt completely is 2100 J. The water, when cooled to freezing, releases 2400 J, and if it freezes completely, it releases 5200 J. The calculations indicate that the energy released by the water can heat the ice to its melting point and potentially allow some ice to melt, suggesting that both ice and water coexist at equilibrium. Therefore, the final equilibrium state consists of both ice and water present in the system.
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Please help/confirm.

You are mixing water with ice in an insulated container. The following are given:

*the amount of heat absorbed by the ice if heated to its melting point: 400 \rm J,
*the amount of heat absorbed by the ice if it all melts (which includes the heat needed to bring the ice to its melting point): 2100 \rm J,
*the amount of heat given off by the water if cooled to its freezing point: 2400 \rm J, and
*the amount of heat given off by the water if it all freezes: 5200 \rm J.

Based on this information, at equilibrium, which phases are present?

-water only
-ice only
-ice and water

I know that the sum of heat released/absorbed in a system is equal to zero, but I'm not sure how to approach it in this problem.

I thought that the total heat absorbed when ice completely melts is 2100 (which is stated above), so the heat released by water must be equal to this. So water does not freeze and ice melts. This means that water is only present. Is this right?

Thanks.
 
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The ice is initially colder than freezing. Some heat is needed to bring it up to melting temperature.
 
So the energy released by water is used to heat the ice to melting point. Does that mean that 2500J is used by water to heat the ice? Does that leave 5100J left for energy to be released by water, but since it has to be equal to the heat absorbed, 5000J is "released" by water. So is equailibrium results in both ice and water being present?
 
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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