Answer
$$ 49700 \frac{\mathrm{ft}^{2}}{\mathrm{s}^{2} \circ \mathrm{R}}=8310 \frac{\mathrm{m}^{2}}{\mathrm{s}^{2} \circ \mathrm{K}} $$
Work Step by Step
$\begin{aligned} \mathrm{R}_{0} &=\left[49700 \frac{\mathrm{ft}^{2}}{\mathrm{s}^{2} \circ \mathrm{R}}\right] \\ &=\left[49700 \frac{\mathrm{ft}^{2}}{\mathrm{s}^{2} \circ \mathrm{R}}\right]\left[0.0928 \frac{\mathrm{m}^{2}}{\mathrm{ft}^{2}}\right]\left[0.556 \frac{\circ \mathrm{R}}{\circ\mathrm{K}}\right] \\ &=\left[49700 \frac{\mathrm{m}^{2}}{\mathrm{s}^{2} \circ \mathrm{R}}\right]\left[0.0928 \frac{\mathrm{m}^{2}}{\mathrm{ft}^{2}}\right]\left[\frac{9}{5} \frac{ \circ \mathrm{R}}{\circ \mathrm{K}}\right] \\ & \approx 8310 \frac{\mathrm{m}^{2}}{\mathrm{s}^{2} \circ \mathrm{K}} \\ & \therefore 49700 \frac{\mathrm{ft}^{2}}{\mathrm{s}^{2} \circ \mathrm{R}}=8310 \frac{\mathrm{m}^{2}}{\mathrm{s}^{2} \circ \mathrm{K}} \end{aligned}$
