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 $$0.5W/m$$∘C. The surface area of tank in contact with water is $$0.05m2$$. 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). (Take$$ $$g=10m/s2$$ $$)

Question

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 $$0.5W/m$$∘C. The surface area of tank in contact with water is $$0.05m2$$. 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).  (Take$$ $$g=10m/s2$$ $$)

Infinity Learn · Accepted Answer

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 dθ$$dt=kAT2$$−$$T1x=0.5$$×$$0.05$$×$$12$$×$$10$$−$$3=12.5$$ Js.for steady temperature of water           Mg ⁡$$v=12.5$$                                              $$M=12.510$$×$$0.1=12.5kg$$

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