Question

A synthetic oil melts at 100 K, boils at 200 K, has a latent heat of fusion of 100 kJ/kg, a latent heat of vaporization of 1 MJ/kg, a solid specific heat of 1000 J/kgK, liquid specific heat of 2000 J/kgK, and vapor specific heat of 3000 J/kgK. Find the final state and temperature if 950 kJ of heat are added to 5 kg of the solid at 90 K.

Answer 1

Heat required to go from solid at 90 K to solid at 100 K, H₁ = mc = 5*1000*10 = 50000 J = 50 kJ

As this is less than 950 kJ, the remaining heat (900 kJ) starts melting the solid.

Heat needed to melt , H₂ = mL = 5*100 kJ = 500 kJ

This is again less than the heat given which means that the solid melts completely at 100 K and still 400 kJ of heat is left.

Then the liquid goes from 100 K to 200 K and heat needed is, H₃ = mc = 5*2000*100 = 1000000 J = 1000 kJ

Now, the amount of heat given is less than 1000 kJ, which means the liquid will not go upto 200 K. Now we calculate the final temperature.

H = 400 kJ = mc = 5*2000*(T - 100)

T - 100 = 40 K

T = 140 K

Therefore, the oil is finally in the liquid state and its temperature is 140 K

I hope i was able to answer your question. If you need anymore explanation, please ask in comments. I would be happy to help.

Please rate the solution if you are satisfied with the solution.