Ice cube into water/thermal equilibrium

In summary, after equilibrium is reached, the glass will contain 170 g of water and 30 g of ice at a temperature of 0°C. The volume of the glass is given to prevent spillage when filling it with ice and water. The equations used are (dQ)=mc(dT), specific heat of water= 1.00 (cal/gK), latent heat of fusion for ice= 79.6 (cal/g), and specific heat of ice= 0.5 (cal/gK). The final temperature of the mixture is determined by balancing the amount of heat needed to melt the ice and the amount of heat lost by the water to reach 0°C.
  • #1
farmerburns
5
0

Homework Statement



A 400 cm3 glass is filled with 100 g of ice at 0°C and 170 g of water at 25°C.

Characterize the content of the glass after equilibrium has been reached. Neglect heat transfer to and from the environment.

_ g (mass of water)
_ g (mass of ice)
_°C (equilibrium temperature)



Homework Equations



(dQ)=mc(dT)
specific heat of water= 1.00 (cal/gK)
latent heat of fusion for ice= 79.6 (cal/g)
specific heat of ice= 0.5 (cal/gK)?




The Attempt at a Solution



I have tried this as many ways as I can think of. First off, is volume even an issue? Second, do I need to use heat of fusion to find the final temp.? I feel very lost.
 
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  • #2
m(w)*C*(T2-T1) = m(i)*L + m(i)*T1
The volume of the glass is given to make shure that water will not spill out of the glass when ice and water is filled in the glass.
 
  • #3
rl.bhat said:
m(w)*C*(T2-T1) = m(i)*L + m(i)*T1
The volume of the glass is given to make shure that water will not spill out of the glass when ice and water is filled in the glass.

Using the given equation I get T2=71.8C. Seems a bit high to me. Any other suggestions? I used intial temp. of water=25C, and initial temp of ice=0C.
 
  • #4
Amount of heat needed to melt the ice = 100*79.6 cal.
Heat lost by the water to reach 0 degree C is = 175*25 cal, which is less than the above. So the ice does not melt completely. Final temperature of the mixture is zero.
 
  • #5
yes, you are right, thank you. I figured it out today with some help.
 

What is the process of an ice cube melting into water?

When an ice cube is placed in a warmer environment, heat from the surroundings is transferred to the ice cube. This causes the ice cube to absorb energy and increase in temperature. As the temperature of the ice cube rises, its molecules begin to vibrate more rapidly and break free from their fixed positions, turning into liquid water.

How does thermal equilibrium occur when an ice cube melts into water?

When an ice cube is placed in a warmer environment, thermal equilibrium occurs when the temperature of the ice cube and water reaches the same level. At this point, the rate of heat transfer between the surroundings and the ice cube is equal, resulting in no further change in temperature.

Why does the temperature of the ice cube not rise above 0 degrees Celsius while it is melting into water?

Even though heat is being transferred to the ice cube, its temperature remains at 0 degrees Celsius until it has completely melted into water. This is because the energy from the surroundings is being used to break the bonds between the molecules of the ice, rather than increasing its temperature.

What factors affect the rate at which an ice cube melts into water?

The rate at which an ice cube melts into water can be affected by various factors such as the temperature of the surroundings, the size and shape of the ice cube, and the material of the container holding the ice cube. Higher temperatures and larger surface areas typically result in a faster melting rate.

Can an ice cube melt into water without any heat being added?

No, an ice cube cannot melt into water without the addition of heat. This is because melting is a process that requires energy to break the bonds between the molecules of ice. Without any external heat source, the surroundings would be at a lower temperature than the ice cube, resulting in a decrease in temperature and no melting.

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