Question

a large kitchen pot initially contains 7.5 kg of water at a burner is turned on and heated

heat Is 1.2.6. A large kitchen pot initially contains 7.5 kg of water at 20°C. A burner is turned on and added to the water at a rate of 500 cal/s. Determine how many minutes it will take for one-third of the mass to evaporate at standard atmospheric pressure.

Answer 1

Specific heat of water $C=4186\,K/kg.\degree C$

Latent heat of vaporization of water $L=2260*10^3\,J/kg$

Amount of heat required to raise temperature of $m=7.5\,kg$ of water at $20\degree C$ to $100\degree C$ and then evaporating one-third $(2.5\,kg)$ of water is $Q=mC\Delta T+m_{evaporated}L$

$Q=7.5*4186*80+2.5*2260*10^3=8161600\,J$

Rate at which heat is added is $\frac{dQ}{dt}=500\,cal/s=2092\,J/s$

Time taken for the mass to evaporate to one-third is $t=\frac{Q}{\frac{dQ}{dt}}=\frac{8161600}{2092}=3901\,s=65\,min$