222 ENGINEERING THERMODYNAMICS
dharm
/M-therm/Th4-7.pm5- 1 kg of air at 1.02 bar, 20°C is compressed reversibly according to a law pv1.3 = constant, to a pressure of
5.5 bar. Calculate the work done on the air and heat flow to or from the cylinder walls during the
compression. [Ans. 133.5 kJ/kg ; – 33.38 kJ/kg] - 0.05 kg of carbon dioxide (molecular weight 44), occupying a volume of 0.03 m^3 at 1.025 bar, is compressed
reversibly until the pressure is 6.15 bar. Calculate final temperature, the work done on the CO 2 , the heat
flow to or from the cylinder walls,
(i) When the process is according to law pv1.4 = constant,
(ii) When the process is isothermal,
(iii) When the process takes place in a perfectly thermally insulated cylinder.
Assume CO 2 to be a perfect gas, and take γ = 1.3. Ans.270 C ; 5.138 kJ ; 1.713 kJ ; 52.6 C ; 5.51 kJ ;
5.51 kJ ; 219 C ; 5.25 kJ ; 0 kJ
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NMO
QP- Oxygen (molecular weight 32) is compressed reversibly and polytropically in a cylinder from 1.05 bar, 15°C
to 4.2 bar in such a way that one-third of the work input is rejected as heat to the cylinder walls. Calculate
the final temperature of the oxygen.
Assume oxygen to be a perfect gas and take cv = 0.649 kJ/kg K. [Ans. 113°C] - A cylinder contains 0.5 m^3 of a gas at 1 × 10^5 N/m^2 and 90°C. The gas is compressed to a volume of 0.125 m^3 ,
the final pressure being 6 × 10^5 N/m^2. Determine :
(i) The mass of gas.
(ii) The value of index ‘n’ for compression.
(iii) The increase in internal energy of gas.
(iv) The heat received or rejected by the gas during compression.
(γ = 1.4, R = 294.2 Nm/kg°C). [Ans. 0.468 kg ; 1.292 ; 62.7 kJ ; – 22.67 kJ]
Steady Flow Systems
- 12 kg of a fluid per minute goes through a reversible steady flow process. The properties of fluid at the inlet
are p 1 = 1.4 bar, ρ 1 = 25 kg/m^3 , C 1 = 120 m/s and u 1 = 920 kJ/kg and at the exit are p 2 = 5.6 bar, ρ 2 = 5
kg/m^3 , C 2 = 180 m/s and u 2 = 720 kJ/kg. During the passage, the fluid rejects 60 kJ/s and rises through 60
metres. Determine : (i) the change in enthalpy (∆h) and (ii) work done during the process (W).
[Ans. ∆h = – 93.6 kJ/kg ; W = – 44.2 kW] - In the turbine of a gas turbine unit the gases flow through the turbine is 17 kg/s and the power developed
by the turbine is 14000 kW. The enthalpies of the gases at inlet and outlet are 1200 kJ/kg and 360 kJ/kg
respectively, and the velocities of the gases at inlet and outlet are 60 m/s and 150 m/s respectively. Calculate
the rate at which the heat is rejected from the turbine. Find also the area of the inlet pipe given that the
specific volume of the gases at inlet is 0.5 m^3 /kg. [Ans. 119.3 kW (heat rejected) ; 0.142 m^3 ] - Air flows steadily at the rate of 0.4 kg/s through an air compressor, entering at 6 m/s with a pressure of
1 bar and a specific volume of 0.85 m^3 /kg, and leaving at 4.5 m/s with a pressure of 6.9 bar and a specific
volume of 0.16 m^3 /kg. The internal energy of air leaving is 88 kJ/kg greater than that of the air entering.
Cooling water in a jacket surrounding the cylinder absorbs heat from the air at the rate of 59 kJ/s. Calculate
the power required to drive the compressor and the inlet and outlet pipe cross-sectional areas.
[Ans. 104.4 kW ; 0.057 m^2 ; 0.014 m^2 ] - A turbine operating under steady flow conditions receives steam at the following state : pressure
13.8 bar ; specific volume 0.143 m^3 /kg ; internal energy 2590 kJ/kg ; velocity 30 m/s. The state of the
steam leaving the turbine is : pressure 0.35 bar ; specific volume 4.37 m^3 /kg ; internal energy 2360
kJ/kg ; velocity 90 m/s. Heat is lost to the surroundings at the rate of 0.25 kJ/s. If the rate of steam
flow is 0.38 kg/s, what is the power developed by the turbine? [Ans. 102.8 kW] - A nozzle is a device for increasing the velocity of a steadily flowing stream of fluid. At the inlet to a certain
nozzle the enthalpy of the fluid is 3025 kJ/kg and the velocity is 60 m/s. At the exit from the nozzle the
enthalpy is 2790 kJ/kg. The nozzle is horizontal and there is negligible heat loss from it.
(i) Find the velocity at the nozzle exit.
(ii) If the inlet area is 0.1 m^2 and specific volume at inlet is 0.19 m^3 /kg, find the rate of flow of fluid.