Transfer of Heat: mass of liquid helium that boils?

In summary, in this conversation, the topic of discussion is the storage of liquid helium at its boiling point temperature of 4.2 K in a spherical container with a radius of 0.251 m. The container is a perfect blackbody radiator and is surrounded by a spherical shield with a temperature of 72.8 K. A vacuum exists between the container and shield. The question being asked is what mass of liquid helium will boil away through the venting valve in 19.2 hours, given the specific heat and latent heat of vaporization for helium. The correct method of solving this problem involves calculating the net power using the Stefan-Boltzmann Law and the correct area, then using the power and time to find the
  • #1
MKM
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Liquid helium is stored at its boiling-point temperature of 4.2 K in a spherical container (r = 0.251 m). The container is a perfect blackbody radiator. The container is surrounded by a spherical shield whose temperature is 72.8 K. A vacuum exists in the space between the container and shield. The latent heat of vaporization for helium is 2.1 x 104 J/kg. What mass of liquid helium boils away through the venting valve in 19.2 hours?


I have tried calculating the net Powere first withthe equation Pnet =e sigma (5.67*E -8) A(.251*.251*pi) ( T^4-Tenvirnment^4) this gives me
.315210793711 as my Pnet. then I plug it into the formula Q=Pt Q=P*69120 secs) = 21787.3700613. My last step is to plug it into Q=mLv which is my new specific heat divided by my liquid heat of vaoprization of helium which is 2.1*E4 I get 1.03749, which is incorrect. I am not sure where I am going wrong . should I be calculating separate Q values from the beginning with different e values?
 
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  • #2
For one thing the area of a sphere is 4[itex]\pi[/itex]r2.

So one calculates the P (W) from the Stefan-Boltzmann Law - using the correct area.

Then with power * time = Q, and one can then use the latent heat to find the mass.
 
  • #3


There are a few issues with your calculations. First, the equation Pnet =e sigma A (T^4-Tenvironment^4) is not applicable in this scenario because it assumes a constant temperature for the object, which is not the case in this situation. The temperature of the helium in the container will decrease over time as it loses heat to the surroundings, so the net power calculation needs to take this into account.

Secondly, the equation Q=Pt is not applicable either because it assumes a constant power over time, which is not the case here. The power is also changing over time as the temperature of the helium changes.

To accurately calculate the mass of helium that boils away, you will need to use the heat transfer equation Q=mCpΔT, where Cp is the specific heat of helium. This equation takes into account the changing temperature of the helium and the specific heat of the substance.

Additionally, the specific heat of helium is not the same as the latent heat of vaporization. Latent heat is the amount of heat required to change the state of a substance (in this case, from liquid to gas) without changing its temperature. The specific heat, on the other hand, is the amount of heat required to change the temperature of a substance by 1 degree.

In order to accurately calculate the mass of helium that boils away, you will need to use the heat transfer equation with the specific heat of helium and take into account the changing temperature of the helium over time. You may also need to consider the heat transfer through the container and shield walls, as well as any heat losses due to radiation or convection. It is a complex calculation and may require more information or assumptions about the system.
 

1. What is the transfer of heat?

The transfer of heat is the movement of thermal energy from a warmer object to a cooler object. This can occur through conduction, convection, or radiation.

2. How is heat transferred in the boiling of liquid helium?

In the boiling of liquid helium, heat is transferred through convection. As the liquid helium is heated, the molecules gain energy and move faster, causing them to spread out and rise to the top of the container. This movement of the heated molecules transfers heat to the cooler molecules at the surface, causing them to also gain energy and eventually boil.

3. What factors affect the mass of liquid helium that boils?

The mass of liquid helium that boils is affected by the amount of heat being transferred, the temperature of the surrounding environment, and the pressure of the container. Higher temperatures and lower pressures will result in more liquid helium boiling.

4. Is the transfer of heat reversible?

In most cases, the transfer of heat is reversible. This means that if the heat source is removed, the temperature of the object will eventually return to its original state. However, some processes, such as irreversible chemical reactions, can result in a permanent transfer of heat.

5. How does the transfer of heat relate to the laws of thermodynamics?

The transfer of heat is governed by the laws of thermodynamics, which state that energy cannot be created or destroyed, only transferred or converted from one form to another. This means that the total amount of energy before and after a transfer of heat must remain constant.

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