Calculating Enthalpy and Internal Energy of Melting Ice

In summary, the latent heat of ice is 80cal/g and the densities of ice and water are 0.9168 and 0.9998g/cm3, respectively. The change in enthalpy and internal energy for melting 1kg of ice at 0*C can be calculated using the formulas ΔH = ΔU + pΔV and V = m/ρ.
  • #1
edimeo25
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The densities of ice and water at 0*C are 0.9168 and 0.9998g/cm3. The latent heat of ice is 80cal/g. What is "delta"H and "delta"U (enthalpy and internal energy, respectively) when 1kg of ice is melted?

I'm really confused on which formulas to use and if the densities are even relevant to this question. One of the formulas I was looking at are "delta"U = m x Cv x "delta"T (but because "delta"T is zero, this would make the variation of internal energy 0, which doesn't make much sense, does it?)

Any help would be greatly appreciated! Thanks in advance.

EricADDITION:
I just read the FAQ sticky note for this section and I'm sorry for not including my attempts thus far. I'm new to the forum and wasn't completely aware of what's expected. So here goes:

One thing I tried was using the formula described above but it doesn't seem to make sense that the internal energy wouldn't change.
Another formula I tried was the following:
H = U + pV

Where V = 0.9168g/cm3 / 1000g = 9.168 x 10^-4 cm3
But now I still don't have V and the question doesn't specify the pressure (I could assume we're at atmospheric pressure, but I'm still no further ahead)
I feel like the answer is really simple and I'm just making it complicated. Any insight would be great!
 
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  • #2
The key is H = U + pV, and from that ΔH = ΔU + Δ(pV), which given p is constant becomes, ΔH = ΔU + pΔV. Unless otherwise stated, one would assume ambient or atmospheric pressure (~1 atm).

From the problem statement, "latent heat of ice is 80cal/g" or heat of fusion, or change in enthalpy from ice to water requires 80 cal/g. One is also given the mass.

BTW, volume = m/ρ. One can find the change of volume of ice to volume of water. The densities are given for both.
 

Related to Calculating Enthalpy and Internal Energy of Melting Ice

What is enthalpy and internal energy?

Enthalpy is a thermodynamic property that describes the total energy of a system, including both its internal energy and the energy required to overcome pressure and volume changes. Internal energy is the sum of all the microscopic energies of a system's particles, including their kinetic and potential energies.

How do you calculate the enthalpy and internal energy of melting ice?

The enthalpy of melting ice can be calculated using the equation Q = mL, where Q is the heat energy required to melt the ice, m is the mass of the ice, and L is the latent heat of fusion of water. The internal energy can be calculated using the equation ΔU = Q + W, where ΔU is the change in internal energy, Q is the heat energy, and W is the work done on the system.

What is the significance of calculating the enthalpy and internal energy of melting ice?

Calculating the enthalpy and internal energy of melting ice is important in understanding the thermodynamics of phase changes and the behavior of substances at different temperatures. It is also useful in various industrial processes, such as refrigeration and freezing, and in environmental studies.

What factors can affect the enthalpy and internal energy of melting ice?

The enthalpy and internal energy of melting ice can be affected by factors such as the initial temperature of the ice, the pressure and volume of the system, and any external work or heat applied to the system. Additionally, impurities in the ice or changes in the surrounding environment can also affect these values.

Can the enthalpy and internal energy of melting ice be negative?

Yes, the enthalpy and internal energy of melting ice can be negative if the system is losing heat energy during the phase change. This can occur if the initial temperature of the ice is above its melting point, or if the system is in an environment with a lower temperature than the melting ice.

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