An ordinary vapor compression cycle is to be operated on methane to cool a chamb

Question

An ordinary vapor compression cycle is to be operated on methane to cool a chamber to 112 K. Heat is rejected to liquid ethylene at 160 K. The temperatures in the coils are 168 K and 100 K. (ANS. online) Write the relevant energy and entropy balances for the compression step. Estimate the minimal work requirement (J/g) for the compressor assuming the ideal gas law. Estimate the coefficient of performance (COP) for this OVC cycle. Estimate the COP by the Carnot guideline. Estimate the minimal work requirement for the compressor using the chart in

Explanation / Answer

Temperature in the coils, T1 = 168 K and T2 = 100 K

b) Minimal Work Requirement is the minimum amount of work which can be done, and it is defined as:

pV = nRT (according to the Ideal Gas Law)

where V is the volume in litres,

P is the pressure in atm,

n is the number of moles

R is the gas constant, 0.8321 L atm/ moles K

T is the temperature in K

c) Coefficient of Performance, COP = Q/ W

Where Q is the Heat Output from the compressor and W is the Power supplied to the compressor

COP = 160 K/ (168 - 100) K

= 160/68 = 2.35

d) Considering the Carnot Guideline or Carnot Efficiency, the COP is given as:

COP = TCond / TCond - TEvap

   Here, TCond is the condensation temperature and TEvap is the evaporation temeprature

COP = 112 K/ (160 - 112)K

= 112 K / 48 K = 2.33

Chart is missing and complete information will provide the answer through the implementation of the above mentioned formulas.

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