Fork pushed into ice (thermodynamics, clausius clapeyron)

In summary: Using the Clausius-Clapeyron equation, he can calculate the pressure exerted on the ice and the gradient of the phase boundary between water and ice. By assuming linearity of the phase boundary and solving for temperature, Chetan can determine the temperature at which the ice will resist penetration. However, this method relies on the assumption that L and the density of ice and water do not vary significantly with temperature and pressure.
  • #1
Robsta
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Homework Statement


A person (mass 57.8 kg) tries to penetrate a garden fork (mass 1 kg) into a melting block of ice by standing on it with all his/her weight. Assume that no heat flows from the fork to the ice. The fork has four prongs, and each prong has a square cross section of area 1 mm2 . By how much must the temperature of the ice be lowered to resist penetration? [You may take the density of water and ice at 0 °C to be 1000 kg m−3 and 916.7 kg m−3 , respectively. The latent heat of fusion of ice is 333 × 103 J kg−1 .]

Homework Equations


The Clausius-Clapeyron Equation gives the gradient of the phase boundary between water and ice.

dp/dT = L/TΔV

The Attempt at a Solution


I can work out what the pressure exerted on the ice is, that's fine. I just use the weight of the person and fork and divide it by the area. This pressure will melt the ice into water and penetrate if the ice is not too cold.

I can also calculate L/ΔV from information given at the end of the question. So the gradient of the phase boundary is just (L/ΔV)/T

Perhaps if I say the ice is solid at p = 105Pa and T = 273 K and then assume that the phase boundary is linear, then I can say Δp/ΔT = dp/dT = L/TΔV and solve for T. Then I know the temperature at which the ice is on the point of melting for the given pressure. If the ice is colder than that, it won't be penetrated.

Does that sound right? It seems like I'm making a big assumption about the linearity of the phase boundary over a wide range of pressures.
 
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  • #2
Robsta said:

The Attempt at a Solution


Does that sound right?
Yes.
It seems like I'm making a big assumption about the linearity of the phase boundary over a wide range of pressures.
How much do you think L changes with temperature and pressure?
How much do you think the density of ice and liquid water change with temperature and pressure?

Chet
 

1. How does a fork pushed into ice demonstrate thermodynamics?

The act of pushing a fork into ice involves the transfer of energy from the fork to the ice. This energy transfer is a fundamental concept in thermodynamics, which is the study of how energy is converted and transferred between different forms. In this case, the energy from the fork is transferred to the ice, causing a change in its temperature and state.

2. What is the significance of the Clausius-Clapeyron equation in this scenario?

The Clausius-Clapeyron equation is a fundamental equation in thermodynamics that describes the relationship between the temperature and pressure of a substance during a phase change. In the case of a fork pushed into ice, this equation helps to explain why the ice melts at a specific rate and why the temperature of the ice changes as the fork is pushed into it.

3. How does the temperature of the ice change as the fork is pushed into it?

As the fork is pushed into the ice, the temperature of the ice increases due to the transfer of energy from the fork. This increase in temperature causes the ice to melt, as it reaches its melting point. Once the fork is removed, the temperature of the ice will decrease again, as it loses the energy it gained from the fork.

4. What happens to the pressure of the ice as the fork is pushed into it?

The pressure of the ice increases as the fork is pushed into it. This is because the fork is exerting a force on the ice, causing it to compress and increase in density. This increase in pressure can also contribute to the melting of the ice, as it can cause the ice to reach its melting point at a lower temperature.

5. How does the fork pushing into the ice relate to the laws of thermodynamics?

The fork pushing into the ice demonstrates the first and second laws of thermodynamics. The first law states that energy cannot be created or destroyed, only transferred or converted from one form to another. In this case, the energy from the fork is transferred to the ice, causing a change in its temperature and state. The second law states that in any energy transfer or conversion, some energy will be lost as heat. In the case of a fork pushing into ice, some of the energy from the fork will be lost as heat to the surrounding environment.

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