In an industrial process, 10 kg of water per hour is to be heated from 20⁰C to 80⁰C. To do this, steam at 150⁰C 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 90⁰C, how many kg of steam is required per hour? (Take, specific heat of steam = 1 cal per g⁰C, latent heat of vaporisation = 540 cal g^-1)

detailed solution

Correct option is B

Suppose m gm steam is required per hour.Heat is released by steam in following three steps: (i) When steam at  150∘C→ steam at 100∘C    Q1=mcsteam Δθ=m×1(150−100)=50m cal (ii) When steam at   100∘C→Q2 water at 100∘C      Q2=mLV=m×540=540mcal(iii) When water at 100∘C→Q2 water at 90∘C    Q3=mcwΔθ=m×1×(100−90)=10mcal     Hence, total heat given by the steam,     Q=Q1+Q2+Q3=600mcal               …(i)    Heat taken by 10 kg water,           Q′=mcwΔθ=10×103×1×(80−20)=600×103 cal     As,   Q=Q′⇒600m=600×103⇒m=103g=1kg