an iron block of unknown mass at 85oc is dropped into an insulated tank that contains 100l of water at 20oc. at the same time, a paddle wheel driven by a 200-w motor is activated to stir the water. it is observed that thermal equilibrium is established after 20min with a final temperature of 24oc. assuming the surroundings to be at 20oc, the mass (in kg) of the iron block is _____. (assume specific heat of iron = 0.45kj/kg-k)
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Let heat carrying capacity of iron block (m × cp) = C
Tfe = 85°C = 358 K
Tw = 20°C = 293 K;
Tf = 24°C = 297 K
Mass of water = 0.1×1000 = 100 kg
W.D by motor in 20 min = 200×20×60 = 240000 J
Heat gain by water = W.D by motor + heat lost by
iron block
Þ 100×4180×(297 – 293) = 240000 + C×(358 – 297)
Þ C = 23475.41 J/K
ΔSwater = 100 × 4.18 × ln(297/293)=5.6679 KJ/K
ΔSFe=23.475xln(297/358)=-4.385 KJ/K
ΔSpadde = 0 because work supplied to a viscous thermally insulated liquid, which is dissipated adiabatically into internal energy increases of liquid, the temperature of which increases from Ti to Tt
\ ΔSuniverse = 5.6679 – 4.3852 + 0
= 1.2827 KJ / K
Tfe = 85°C = 358 K
Tw = 20°C = 293 K;
Tf = 24°C = 297 K
Mass of water = 0.1×1000 = 100 kg
W.D by motor in 20 min = 200×20×60 = 240000 J
Heat gain by water = W.D by motor + heat lost by
iron block
Þ 100×4180×(297 – 293) = 240000 + C×(358 – 297)
Þ C = 23475.41 J/K
ΔSwater = 100 × 4.18 × ln(297/293)=5.6679 KJ/K
ΔSFe=23.475xln(297/358)=-4.385 KJ/K
ΔSpadde = 0 because work supplied to a viscous thermally insulated liquid, which is dissipated adiabatically into internal energy increases of liquid, the temperature of which increases from Ti to Tt
\ ΔSuniverse = 5.6679 – 4.3852 + 0
= 1.2827 KJ / K
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