In an industrial process 10 kg of water per hour is to be heated from 20oC to 80oC. To do this steam at 150oC is passed from a boiler into a copper coil immersed in water. The steam condenses in the coil and is returned to the boiler as water at 90oC. How many kg of steam is required per hour? (Specific heat of steam: specific heat of water = 1 cal/goC; Latent heat of vaporization = 540 cal/g)

Suppose m kg steam is required per hourHeat is released by steam in following three steps (i) When 150∘C steam ⟶100∘C steam Q1=mcsteam Δθ=m×1(150−100)=50mcal (ii) When 100∘C steam ⟶100∘C water Q2=mLv=m×540=540mcal (iii) When 100∘C water ⟶Q290∘C water Q3=mcWΔθ=m×1×(100−90)=10m cal Hence total heat given by the steamQ=Q1+Q2+Q3=600mcal  ………(i)Heat taken by 10 kg waterQ′mcWΔθ=10×103×1×(80−20)=600×103 cal  Hence Q=Q′⇒600m=600×103⇒m=103g=1kg