Project ForgeMass Transfer
Diffusion
GATE 2019
Hard
Two spherical camphor particles (radii 20cm and 5cm) sublime in an air stream. The mass transfer coefficient is proportional to 1/√r(t). Assuming quasi-steady-state and identical ambient conditions, if t1, t2 are the times for complete sublimation, the ratio t1/t2 is (rounded off to one decimal place)
8(± 0.2 accepted)
Explanation
Mass balance: −ρs·4πr²(dr/dt)=(B/√r)·4πr²·ΔC ⟹ √r·dr=−(BΔC/ρs)dt. Integrating from r0 to 0: t_complete=(2/3)r0^1.5·ρs/(BΔC), i.e. t∝r0^1.5. t1/t2=(20/5)^1.5=4^1.5=8.
Source: GATE CH 2019 (2019)
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