13468-11-74P_done

13468-11-74P AID: 1825 | 05/12/2014 Show the ideal-gas rerigeratio! "#"le$ with air as the wor%i!g l&id$ o! T s − diagra' as i! (ig&re )1*+ (or the gi,e! gas rerigeratio! "#"le$ with air as the wor%i!g l&id$ the te' er s e"ii" e!thal #$ a!d ress&re at th i state are i T $ i h $ a!d i P res e"ti,el#+ .se ideal-gas s e"ii" heats o ,ario&s "o''o! gases ta le $ to i!d p c a!d k o air at roo' te' erat&re+ S-e"ii" heat at "o!sta!t -ress&re$ 1+005% %g S-e"ii" heat ratio$ 1+4 p c k = × )a* ress the te' erat&re a!d ress&re relatio! or the ise!tro i" ro"ess 1-2+ ( ) 1 2 2 1 1 k k P T T P − = ÷ ere$ the s e"ii" heat ratio o heli&' is k + S& stit&te 266 or 1 T $ 4 or 2 1 P P $ a!d 1+4 or k to i!d 2 T + ( ) ( ) ( ) 0+4 1+4 2 266 4 385+3 T = = ress the te' erat&re a!d ress&re relatio! or the ise!tro i" ro"ess 4-5+ ( ) 1 5 5 4 k k P T T P − = ÷

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Transcript of 13468-11-74P_done

13468-11-74P AID: 1825 | 05/12/2014

Show the ideal-gas refrigeration cycle, with air as the working fluid, on diagram as in Figure (1).

For the given gas refrigeration cycle, with air as the working fluid, the temperature, specific enthalpy, and pressure at state are , , and respectively.

Use ideal-gas specific heats of various common gases table, to find and of air at room temperature.

(a)

Express the temperature and pressure relation for the isentropic process 1-2.

Here, the specific heat ratio of helium is k.

Substitute 266 K for , 4 for , and 1.4 for k to find .

Express the temperature and pressure relation for the isentropic process 4-5.

Substitute 258 K for , for , and 1.4 for k to find .

Hence, the lowest temperature that can be obtained in this cycle is .

(b)

Express the energy balance equation for the regeneration process.

Here, the specific heat capacity of air at constant pressure is , the energy entering the system is , energy leaving the system is , and the mass flow rate of air is .

Rearrange and substitute 266 K for , 300 K for , 258 K for to find .

Find the COP for the given ideal-gas refrigeration cycle .

Here, the amount of heat per unit mass, removed from the refrigerated space is , the specific work input to the compressor is , and the specific work output from the turbine is .

Substitute 224 K for , 173.6 K for , 395.3 K for , 258 K for , and 266 K for .

Hence, the COP for the given ideal-gas refrigeration cycle is .

(c)

Find the mass flow rate of air for the given ideal-gas refrigeration cycle .

Here, the total rate of heat removed from the refrigerated space is .

Substitute for , for , 224 K for , and 173.6 K for .

Hence, the mass flow rate of air for the given ideal-gas refrigeration cycle is .