A liquid-nitrogen container is constructed from a 1 -cm thick styrofoam sheet with a thermal conductivity of 0.025 J s^ -1 m^ -1 ^ ^ ^ ^ -1 . Liquid nitrogen at 80 K is stored inside. A total area of 0.80 m^2 is in

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Quantrex Academy · Accepted Answer

Correct answer: C. 440 J s^ -1

The rate of heat flow through the styrofoam sheet is given by Fourier's law of heat conduction:

\dfrac{dQ}{dt} = \dfrac{KA(T_2 - T_1)}{d}

Given values are:
Thermal conductivity,

K = 0.025 \text{ J s}^{-1} \text{ m}^{-1} ^{}^{{}^{\circ}}\textC^{-1}

Area,

A = 0.80 \text{ m}^2

Temperature difference,

\Delta T = T_2 - T_1 = 300 \text{ K} - 80 \text{ K} = 220 \text{ K}

Thickness,

d = 1 \text{ cm} = 0.01 \text{ m}

Substituting these values into the formula:

\dfrac{dQ}{dt} = \dfrac{0.025 \times 0.80 \times 220}{0.01}

\dfrac{dQ}{dt} = \dfrac{0.02 \times 220}{0.01}

\dfrac{dQ}{dt} = \dfrac{4.4}{0.01} = 440 \text{ J s}^{-1}

A liquid-nitrogen container is constructed from a 1 -cm thick...

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