How Much Energy is Needed to Convert Water to Ice Using a Carnot Refrigerator?

AI Thread Summary
To convert 50 kg of water at 0 degrees Celsius to ice at the same temperature using a Carnot refrigerator, the energy required is based on the latent heat of fusion. The latent heat of fusion for water is approximately 334,000 J/kg, meaning 16,700,000 J of energy must be removed to freeze the water. The Carnot efficiency must also be considered, as it affects the total energy input needed for the refrigerator to operate. The temperature difference between the water and the room influences the energy calculations. Understanding these principles is crucial for solving the problem effectively.
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Homework Statement


a carnot refrigerator takes heat from water at 0 degree celsius and rejects heat to a room at 27 degree celsius. if 50kg of water at 0 degree celsius is converted to ice at 0 degree celsius. how much energy must be supplied to the refrigerator?

Homework Equations



Sorry, i don't know how to do it... Please help me. i have an exam this coming april and one of the question given in their practise set is regarding this matter.

The Attempt at a Solution



Sorry
 
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Ever heard of latent heat? try finding an equation to do with this
 
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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