Question

(a)Draw the schematic diagram of the working mechanism of a heat engine, heat pump and refrigerator and state the thermal efficiency of each system (b) Figure Q1(b) shows the schematic diagram of a double cascade cycle. Assuming the flow rates in these two separate cascades are the same and the value of the refrigeration effect in the second cascade is equal to the heat rejected in the condenser of the first cascade (QcondenserAQr Qinter), determine (i) the coefficients of performance for the first cascade; (ii) the coefficients of performance for the second cascade; (ii) the coefficients of performance for the overall cascade, (iv) the relationship between coefficients of performance of cascades (v) the overall coefficient of the performance for the whole installation when CPrefA 5 and CPre-7 Qout High-temperature Expansion valve Compressor Cycle B Intermediate heat exchanger Cycle A WeA valve Low-temperature Figure Q1(b): Cascade cycles 1.4 R- 287 J/(kg.K) 1005 J/(kg·K) 718 J/(kg.K) 1 .226 kg/m 3 101.3 kN/m2 Cv po po 288 K 0 1.783 x 105 kg/(m.s)

Answer 1

Schematic Diagram oF Heaotengine Heat engines are cydlic devices that roorks on a cycle to recieve heat from a and converts a 'Part of it into useful ner K ond rejects "the naste heat to Heat onser throughout the noorking cycle takes place by a fluid caed Working fluid s the waste heat to siok Fluld colled Ti, Souree 1 Reaeve heat from a high temperature sourre 2. Convert Parr oFthis heat into useful roxie in the form of rotating shaft 3 Reject the temaining oaste heat to loro ternperata QL s ink 72,sink 4 Operate On a cyde Thermal EfficiencyWork O/p Heat added W Schematic Diagrom of Refrigera tor Refrigerator is o device that hoorks on cyde to transfer heat From a lovo temperature reservoir to high TH temperature reservoir by means of qwoe accephing woosk from external cyde Process: 1) Extracts heat from the space by a refrigerant 2) Accepts external oork to trans fer the temperature to high temperatu ro reservoir a) Rejects the heat at hish temperature reservoir Schematic Diagram of Heat pump Heat pump is a cydic devike used for transferirg heat from a low temperature reservoir to high temperature res esvoir by means of external ook Process is same as refrigera tor The ony difference is the clesired effect Here our TH nW HP desired effect is he ating Cop

igh emp cond 2 Expansion alve Hea1exchanger Expansion valve condensoi 6in Schematic Diagrom oF Casca de system TH For cyde A Ginter in+ WeA Wee inter COPA Bin WCA Qinter Qin (j) tin COP of First cascade (COP)A 兀 (i) cop of 2nd cascade = 6(inter CoP)p (M) COP of overall cascade. air WcAt Wce Bin in十 COP CORA-COP 8 COPA CO I+ COPA COPs the (COP)ov= 5x7- = 3S"-2692 l tら+7 13