Questions

# Figure shows a paddle wheel coupled with an agitator submerged in a water tank placed in an ice bath. The thickness of tank walls is 2mm and with thermal conductivity $0.5\mathrm{W}/{\mathrm{m}}^{\circ }\mathrm{C}$. The surface area of tank in contact with water is $0.05{\mathrm{m}}^{2}$. As the block of mass M attached to wheel goes down agitator rotates. It is found that in steady state block goes down at a constant speed of 0.1m/s and water temperature remain constant at 1°C. Find the mass of block (in kg).

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a
14.5
b
16.5
c
12.5
d
11.5
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detailed solution

Correct option is C

rate of loss in gravitational  potential energy of block is equal to the rate of heat conduction from water to ice bath as Twater =constant.rate of loss of gravitational P.E. is = Mg vrate of the thermal conduction dθdt=kAT2−T1x=0.5×0.05×12×10−3=12.5 Js.for steady temperature of water           Mg ⁡v=12.5                                              M=12.510×0.1=12.5kg

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