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Question

# Assume that because of in creasing $\mathrm{CO}_{2}$ concentration in the atmosphere, the net radiation energy transfer rate for Earth and its atmosphere is $+0.002 \times 1350 \mathrm{W} / \mathrm{m}^{2}$,corresponding to a 0.2% decrease in radiation leaving Earth. (a) Determine the extra thermal energy added to Earth and its atmosphere in 10 years. [Note:The radiation falls on an area approximately equal to $\pi r_{\text { Earth }}^{2}$ where $r_{\text { Earth }}=6.4 \times 10^{6} \mathrm{m.} ]$ (b) If 30% of this energy is used to melt the polar ice caps, how many kilograms of ice will melt in 10 years? (c) How many cubic meters of ice will melt? (d) By how much will the level of the oceans rise in 10 years?

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$\text{\color{#4257b2}Climate change and controlling body temperature:}$

$\text{\color{#4257b2}Putting it all together}$

$\text{\color{#4257b2}Global climate change }$

$\textbf{(a) Thermal energy that fails to leave earth;}$

The net positive change in thermal energy due to earth retaining additional radiated energy, in terms of the rate of energy transfer per unit area; $\dfrac{H}{A}$;

\begin{align*} \Delta U_{\text{thermal}}&=\dfrac{H}{A}\cdot A\Delta t \\ &=\dfrac{H}{A}\cdot\pi r_{\text{earth}}^{2}\Delta t \\ &=0.002\cdot1350\cdot \pi (6.4\times10^{6})^{2}\cdot10\cdot365\cdot24\cdot(60)^{2} \\ \Delta U_{\text{thermal}}&=1.1\times10^{23}\mathrm{\ J} \end{align*}

$\textbf{(b) Mass of ice melted;}$

If 30% of this thermal energy melts the polar ice caps then using the fusion equation and the result from (a);

\begin{align*} m&=\dfrac{0.3\Delta U_{\text{thermal}}}{L_{\text{v}}} \\ &\overset{\text{note 1.}}{=}\dfrac{0.3\cdot1.1\times10^{23}}{3.35\times10^{5}} \\ m&=9.8\times10^{16}\mathrm{\ kg} \end{align*}

note 1. Latent heat of fusion at melting temperature of water; $L_{\text{v}}=3.35\times10^{5}\mathrm{\ J/kg}$; (Refer to Table 12.7 AP edition)

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