Transmission Of Heat Question 102

Question: There is formation of layer of snow $ x,cm $ thick on water, when the temperature of air is $ -{{\theta }^{o}}C $ (less than freezing point). The thickness of layer increases from $ x $ to $ y $ in the time $ t $ , then the value of $ t $ is given by

Options:

A) $ \frac{(x+y)(x-y)\rho L}{2k\theta } $

B) $ \frac{(x-y)\rho L}{2k\theta } $

C) $ \frac{(x+y)(x-y)\rho L}{k\theta } $

D) $ \frac{(x-y)\rho Lk}{2\theta } $

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Answer:

Correct Answer: A

Solution:

Since $ t=\frac{\rho L}{2k\theta }(x _{2}^{2}-x _{1}^{2}) $

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Therefore $ $ t=\frac{\rho L}{2k\theta }(x^{2}-y^{2})=\frac{\rho L(x+y)(x-y)}{2K\theta } $