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To understand the amount of liquid helium that evaporates due to radiation, we start with the Stefan-Boltzmann Law. This law is an essential principle in thermal physics which describes the power radiated by a black body in terms of its temperature. The formula is given by \( Q = e \sigma A(T_1^4 - T_2^4) \). Here, \( e \) stands for emissivity, \( \sigma \) is the Stefan-Boltzmann constant (approximately \(5.67 \times 10^{-8} W/(m^2 K^4)\)), \( A \) is the surface area, and \( T_1 \) and \( T_2 \) represent the temperatures of the object and its surroundings respectively.

In our problem, the can storing the helium has a specific surface area due to its cylindrical shape. The temperatures \( T_1 \) and \( T_2 \) are the temperatures of the helium and the surrounding walls, respectively. By understanding this relationship, we can calculate how much energy in the form of radiation is lost from the can, hence leading to the vaporization of liquid helium. This energy loss plays a crucial role in how long the helium stays in its liquid state.

Using the Stefan-Boltzmann Law, we can precisely determine the rate of energy loss, which can then be converted to the mass of helium that boils off every hour.

Emissivity is a measure of an object's ability to emit thermal radiation. It is a ratio that ranges from 0 to 1, where 1 indicates a perfect black body that emits all possible radiation. In real-world applications, no object is a perfect black body, and thus we use values less than 1.

In this specific problem, the metal can has an emissivity value of 0.200. This means it radiates only 20% of the energy that a perfect black body would at the same temperature. Understanding emissivity is crucial because it directly affects the heat transfer due to radiation. Lower emissivity means less heat loss through radiation, which in turn influences how much helium evaporates.

By incorporating the emissivity factor into the Stefan-Boltzmann equation, we can calculate a more realistic figure for the energy loss experienced by the can. This allows us to accurately predict how much liquid helium will turn into gas over a given period of time.

The heat of vaporization is the amount of energy required to convert a unit mass of a liquid into vapor without a temperature change. For helium, it is specified as \(2.09 \times 10^4 J/kg\).

This property is particularly important in understanding how much energy is needed to turn liquid helium into its gaseous form. Essentially, whenever the energy absorbed by the liquid helium is equal to or greater than the heat of vaporization, a portion of it will evaporate.

In our problem, once we know the rate of heat loss via radiation, we can use the heat of vaporization to determine how much mass of helium is turned into gas. By using the formula \( \Delta Q = m \Delta H \), with \( \Delta Q \) being the heat lost per hour, we can calculate the mass \( m \) of helium evaporated.

This heat-intensive process demonstrates just how significant the role of thermal energy transfer is in practical applications involving cryogenic substances like helium.

Thermal physics is an interdisciplinary field encompassing the physiological consequences of heat transfer, thermodynamics, and statistical mechanics. It's central to understanding phenomena where heat plays a crucial role, such as radiation heat transfer.

In our scenario, thermal physics principles guide us through analyzing how the environment controls the state of the helium. By studying these principles, one can see how factors such as temperature differences, surface area, and material properties (like emissivity) combine to produce the observed effects.

Understanding the concepts of heat exchange is critical when dealing with extreme temperatures, like those in cryogenics. The scenario with the helium involves designing systems to manage and mitigate undesired heat transfer to prolong the liquid state of cryogenic substances.

Thermal physics offers the tools to quantify and optimize these systems, ensuring efficiency in applications like the storage and transport of liquid helium, exemplifying the practical application of theoretical principles.