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# Hot coffee is contained in a cylindrical thermos bottle that is of length L=0.3 m and is lying on its side (horizontally). The coffee container consists of a glass flask of diameter $D_{1}=0.07 \mathrm{m}$, separated from an aluminum housing of diameter $D_{2}=0.08 \mathrm{m}$ by air at atmospheric pressure. The outer surface of the flask and the inner surface of the housing are silver coated to provide emissivities of $\varepsilon_{1}=\varepsilon_{2}=0.25$. If these surface temperatures are $T_{1}=75^{\circ} \mathrm{C}$ and $T_{2}=35^{\circ} \mathrm{C}$, what is the heat loss from the coffee?

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$\textbf{We are given following data:}$

\begin{align*} T_{1}&=75\text{\textdegree}\mathrm{~C}\\ &=75+273\\ &=348\mathrm{~K}\\ T_{2}&=35\text{\textdegree}\mathrm{~C}\\ &=35+273\\ &=308\mathrm{~K}\\ D_{1}&=0.07\mathrm{~m}\\ R_{1}&=\dfrac{D_{1}}{2}\\ &=\dfrac{0.07m}{2}\\ &=0.035\mathrm{~m}\\ D_{2}&=0.08\mathrm{~m}\\ R_{2}&=\dfrac{D_{2}}{2}\\ &=\dfrac{0.08m}{2}\\ &=0.04\mathrm{~m}\\ \epsilon_{1} &=\epsilon_{2} =0.25\\ L &=0.3\mathrm{~m}\\ \end{align*}

$\textbf{Required:}$

• $\text{Heat loss from the coffee $(q_{net})$}$

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