Question

In vacuum insulated cryogenic vessels (Dewars), the major source of heat transferred to the inner container is by radiation through the vacuum jacket. A technique for reducing this is to place "heat shields" in the vacuum space between the inner and outer containers. Idealize this situation by considering two infinite sheets with emissivity $=1$ separated by a vacuum space. The temperatures of the sheets are $T_1$ and $T_2\left(T_2>T_1\right)$. Calculate the energy flux (at equilibrium) between them. Consider a third sheet (the heat shield) placed between the two which has a reflectivity of $R$. Find the equilibrium temperature of this sheet. Calculate the energy flux from sheet 2 to sheet 1 when this heat shield is in place. For $T_2=$ room temperature, $T_1=$ liquid He temperature ( 4.2 K ) find the temperature of a heat shield that has a reflectivity of $95 \%$. Compare the energy flux with and without this heat shield. $$ \left(\sigma=0.55 \times 10^{-7} \text { watts } / \mathrm{m}^2 \mathrm{~K}\right) $$ FIGURE CAN'T COPY.

   In vacuum insulated cryogenic vessels (Dewars), the major source of heat transferred to the inner container is by radiation through the vacuum jacket. A technique for reducing this is to place "heat shields" in the vacuum space between the inner and outer containers. Idealize this situation by considering two infinite sheets with emissivity $=1$ separated by a vacuum space. The temperatures of the sheets are $T_1$ and $T_2\left(T_2>T_1\right)$. Calculate the energy flux (at equilibrium) between them. Consider a third sheet (the heat shield) placed between the two which has a reflectivity of $R$. Find the equilibrium temperature of this sheet. Calculate the energy flux from sheet 2 to sheet 1 when this heat shield is in place.

For $T_2=$ room temperature, $T_1=$ liquid He temperature ( 4.2 K ) find the temperature of a heat shield that has a reflectivity of $95 \%$. Compare the energy flux with and without this heat shield.
$$
\left(\sigma=0.55 \times 10^{-7} \text { watts } / \mathrm{m}^2 \mathrm{~K}\right)
$$
FIGURE CAN'T COPY.
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Problems and Solutions on Thermodynamics and Statistical Mechanics
Problems and Solutions on Thermodynamics and Statistical Mechanics
U.S.T. of China… 1st Edition
Chapter 1, Problem 24 ↓

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** The energy flux \( q \) between two infinite sheets with emissivity \( \epsilon = 1 \) at temperatures \( T_1 \) and \( T_2 \) can be calculated using the Stefan-Boltzmann law: \[ q = \sigma (T_2^4 - T_1^4) \] where \( \sigma = 0.55 \times 10^{-7} \,  Show more…

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In vacuum insulated cryogenic vessels (Dewars), the major source of heat transferred to the inner container is by radiation through the vacuum jacket. A technique for reducing this is to place "heat shields" in the vacuum space between the inner and outer containers. Idealize this situation by considering two infinite sheets with emissivity $=1$ separated by a vacuum space. The temperatures of the sheets are $T_1$ and $T_2\left(T_2>T_1\right)$. Calculate the energy flux (at equilibrium) between them. Consider a third sheet (the heat shield) placed between the two which has a reflectivity of $R$. Find the equilibrium temperature of this sheet. Calculate the energy flux from sheet 2 to sheet 1 when this heat shield is in place. For $T_2=$ room temperature, $T_1=$ liquid He temperature ( 4.2 K ) find the temperature of a heat shield that has a reflectivity of $95 \%$. Compare the energy flux with and without this heat shield. $$ \left(\sigma=0.55 \times 10^{-7} \text { watts } / \mathrm{m}^2 \mathrm{~K}\right) $$ FIGURE CAN'T COPY.
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