A tank volume of 45 cubic meters and contain 40 kg of an ide

A tank volume of 4.5 cubic meters and contain 40 kg of an ideal gas having molecular weight of 38 Kg/Kmol. The temperature is 80 F. Find the special gas constant (R) in KNm/Kg K: Find the pressure (P) in KPa: The coefficient of performance (COP) of Refrigeration cycle is 3.5 and heat transfer of output (Qout) is 1450 KJ. Find the heat transfer of input(Qin) in KJ. Find the net work input (Wcyc) in KJ.

Solution

3]a]

Given:-

v= 4.5m³

m=40 kg

M=38 kg/K mol

T=80 F=[80-32/180]*100 ⁰C= 26.7 ⁰C= 300K

special gas constant , R=R\'/M

R=R\'/M= 8.3145 KNm/Kmol K/38 kg/K mol= 0.219 KNm/Kg.K

3]b]

P=?

PV= nRT

P= nRT/V

P= 1* 0.219*300/4.5= 14.6pa= 0.0146kPa

4]a]

Given:-

COP= 3.5

Q_out=1450 kJ

Q_in= ?

COP=Q_out / W _cycle

W _cycle= Q_in- Q_out

COP=Q_out / [Q_in- Q_out]

[Q_in- Q_out] = Q_out /COP=1450 kJ/ 3.5= 414.29kJ

[Q_in- Q_out] =414.29kJ

Q_in= 414.29kJ +Q_out = 414.29kJ +1450 kJ = 1864.29kJ

Q_in=1864.29kJ

4]b]

W _cycle= Q_in- Q_out

[Q_in- Q_out] =414.29kJ

W _cycle = 414.29kJ