Need help with these questions. It\'s a study guide for an upcoming assignment/t

Question

Need help with these questions. It's a study guide for an upcoming assignment/test.

What is the efficiency of the cycle shown below? A pump with efficiency of 98% at a larger power plant raises the pressure from 3 times 106 N/m3 at 40 degree C to 6 times106 N/m2, if the flow rate is 20,000 kg/min, calculate the power required in W. Air is roughly 21% O2 and 79% of N2 (by volume) calculate the specific heat of air using table values of O2 and N2 and compare your results to the reported values of air from same tables. An air-water vapor mixture at 19 degree C, 50% relative fofflidltY, 101 kPa, is heated to 28 degree C in part of a steady-flow 3,1 conditioning system. Determine the inlet and outlet specific humidities, the discharge Phi and the energy input per kg of dry air

Explanation / Answer

1.

Net work done in cycle W = Area of 2 rectangles

= (600-500)*(0.3 - 0.1) + (700 - 500)*(0.4 - 0.3)

= 40 Btu/lb

Net heat input Q = Area under T = 600 line + Area under T = 700 line

Q = 600*(0.3 - 0.1) + 700*(0.4 - 0.3)

Q = 190 Btu/lb

Efficiency = W/Q

= 40 / 190

= 0.2105 or 21.05 %

2.

Density rho = 1000 kg/m^3

Work done = (P2 - P1)/rho

= (6-3)*10^6 / 1000

= 3000 J/kg

Power = (20,000/60)*3000

= 1*10^6 W

Actual power = 1*10^6 / 0.98

= 1020408 W

3.

Cp_o2 = 919 J/kg-K

Cp_n2 = 1040 J/kg-K

Molecular mass M_o2 = 32

Molecular mass M_n2 = 28

PV = m*R*T

P*V_o2 = m_o2*(R_u / M_o2)*T

P*V_n2 = m_n2*(R_u / M_n2)*T

0.21 / 0.79 = (m_o2 / 32) / (m_n2 / 28)

m_o2 = 0.3038*m_n2

Also,

m_o2 + m_n2 = 1

Solvin them, m_n2 = 0.767 and m_o2 = 0.233

Cp_air = m_o2*Cp_o2 + m_n2*Cp_n2

= 0.767*1040 + 0.233*919

= 1011 J/kg-K

From air tables, Cp = 1005 J/kg-K which is very close to the calculate value.

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