Your friend is designing a compressed air energy storage system for an artic col

Question

Your friend is designing a compressed air energy storage system for an artic colony. Their design uses a solar panel to power an air compressor during the day light hours which charges a canister with air. The canister is rated to 600 atms. During the dark hours the compressor switches off and the compressed air is released through a turbine to recover the energy. Your friend expects the temperature will drop as low as 211 K and will charge the tank to 0.08 L/mol specific volume.

Use both the ideal gas law and a compressibility chart to determine the pressure inside the canister.

Based on the temperatures, is the canister sufficient to hold gas at these conditions?

What advice what suggestions would you give your friend to improve their design?

An equimolar liquid mixture of benzene and toluene at 10oC is fed continuously into a vessel in which the mixture is heated to 50oC. What is the composition of the outlet liquid and vapor states if they exit in equilibrium? If 100 mole/hour are fed into the evaporator, what is the energy requirement to complete this process?

Explanation / Answer

The ideal gas equation is given by:

PV = znRT, where z is the compressibility

if we suppose z=1, for calculating the pressure roughly, we can write,

P = nRT/V

    = 1*0.08205*211/0.08

   = 216.4 atm

now, we can use compressibility table to find z, for T=211 k and P ~ 216.4 atm

we find that z = 1.0185

now using, PV = znRT

                   P = 1.0185*nRT/V

                        = 1.0185*216.4 atm

                       = 220.4 atm

hence, 220.4 atm pressure will develop inside the compressor, which is well within the rated value of 600 atm.

To improve the design, we can give suggestion that air can be pressurised more when it is cold, as it will be easy to compress in cold conditions. That will make compressor more efficient.

For benzene-toluene mixture system,

It may be noted from the boiling point curve of Benzene-Toluene system that, the process of boiling occurs at a temperature not less than 80oC for any composition of liquids. Hence there will be negligible amount of vapours in the outlet. If any, the composition can not be determined using the boiling curve, as the Temperature = 50oC does not lie on the curve. And more data must be required to find the molar concentration from Rault's Law.

for calculating the energy required to heat the mixture,

dT = 40oC

M = 100 moles

Specific Molar heat = Toluene (12 kJ/mol) & Benzene (49 kJ/mol)

hence energy required for heating 50 moles of benzene and 50 moles of toluene (equimolar composition) = (50*12*40 + 50 * 49*40) kJ

                       = 24000 kJ + 98000 kJ

                       = 122 mega Joule.

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