1. 3 kg of a gas at 75°C heated at constant volume until its pressure is 2 times is the initial pressure. Determine the (i) final temperature (ii) heat transfer (iii) change in internal energy and (iv) change in Enthalpy. (Assume Cp = 1.005 kJ/kg K and Cv = 0.718 kJ/kgK)
[Ans:- T2 = 696 K, Q = 741.24 kJ and ΔH = 809.34 kJ]
2. A volume of 28 liters of gas at a temperature of 40°C and pressure of 200 kN/m3. It is heated at constant volume process till the temperature becomes 275°C. Find the (i) mass of the gas (ii) final pressure and (iii) change in enthalpy. Assume Cp = 1.005 kJ/kg K and Cv = 0.718 kJ/kg K.
[Ans:- m = 0.062 kg, p2 = 35015 kN/m2 and ΔH = 10.34 kJ]
3. One kg of gas expands at constant pressure from 0.085 m3 to 0.13 m3. If the initial temperature of the gas is 225°C, find the final temperature, net heat transfer, change in internal energy and pressure of gas.
[Ans:- T2 = 761.6 K, Q = 264.9 kJ, ΔU = 187.16 kJ and p1 = p2 = 1728.3 kN/m2]
4. A certain quantity of gas is heated at constant pressure from 35°C to 185°C. Estimate the amount of heat transferred, ideal work done and change in internal energy when the initial volume of the gas is 0.6 m3. Assume R = 0.3 kJ/kgK and Cp = 1.005 kJ/kgK.
[Ans:- Q = 150.75 kJ, W = 4 5 kJ/kg and ΔU = 105.75 kJ]
5. One kg of gas has a pressure volume and temperature of 2.5 bar, 0.3 m3 and 100°C respectively. It expands isothermally in a cylinder to pressure of 0.75 bar. Estimate the work done by the gas, change in internal energy and heat transferred. Take R = 0.29 kJ/kg K.
[Ans:- W = 130.23 kJ/kg, ΔU = 0 and Q = 130.23 kJ/kg]
6. A certain air at 2 bar pressure and 70°C is compressed to 1/6th of its initial volume isentropically. Determine the final state of the air and work done on 1.8 m3 of air. Assume R = 87 J/kgK.
[Ans:- p2 = 2457.2 kN/m2, T2 = 702.35 K and W = -942.9 kJ]
7. 0.5 kg of a gas expands reversibly and adiabatically from the initial condition of 300 kN/m2 and 195°C. The final pressure of the gas after expansion is 95 kN/m2. The temperature falls by 160°C during the expansion. Calculate the (i) work done during the process (ii) change in internal energy (iii) change in enthalpy and (iv) initial and final volume of gas. Take R = 0.29 kJ/kgK.
[Ans:- W = 57.87 kJ, ΔU =-58 kJ, ΔH = -81.2 kJ, V1 = 0.226 m3 and V2 = 0.47 m3]
8. The initial pressure, volume and temperature of air in a cylinder fitted with a movable piston are 10 bar, 0.04 m3 and 400 K respectively. If air expands according to the law риз pV1.3 = constant to a final volume of 0.2 m3. Calculate the work done, change in internal energy and heat transferred.
[Ans:- W = 51 kJ, ΔU = -38.33 kJ and Q = 12.67 kJ]
9. One kg of ideal gas is heated from 18°C to 93°C. Assuming R = 264 J/kgK, ratio of specific heats 1.18 for the gas and heat transfer of 160 kJ. Find the
(a) value of the specific heats
(b) change in internal energy
(c) change in enthalpy
(d) work transfer.
[Ans:- Cp = 1.73 kJ/kg K, Cv = 1.466 kJ/kg K, ΔU = 109.95 kJ/kg, ΔH = 129.75 kJ/kg and W = 50.05 kJ/kg]
10. A perfect gas for which ratio of specific heats is 1.4 occupies a volume of 0.3 m3 at 100 kPa and 27°C. The gas undergoes compression to 0.06 m3. Find the heat transfer during compression for the following methods of compression (a) pV = constant (b) isentropic. Compare the compression work having molecular weight of gas as 28.
[Ans:- Heat transfer for pV= C, Q = -48.28 kJ/kg, Heat transfer for pVr = C, Q = 0, Work transfer for pV= C, W = -48.28 kJ/kg, Work transfer for pVr = C, W = - 67.78 kJ/kg and compression work of pVr = C is more than the pV= C of the same work].
11. An ideal gas is compressed through a pressure ratio of 10 and the temperature in increased from 30°C to 240°C. Find the (i) polytropic index of compression and (ii) work of compression per unit mass.
[Ans:- n = 1.295, Polytropic compression work and W = -204.3 kJ/kg]
12. Calculate the change internal energy, heat transferred and change in enthalpy for 0.5 kg of air expanding according to law pV1.2 = C from 1 MPa and 300°C to 100 kPa, what will be the work done by air during the expansion?
[Ans:- W = 192.32 kJ, ΔU = 95.69 kJ, Q = 96.16 kJ and ΔH = 134.695 kJ]
13. Air at 475 kPa and 200°C expands in a non-flow process to 75 kPa, as per the law pV1.2 is constant. Find the work done and heat transfer per kg.
[Ans:- W = 179.75 kJ/kg and Q = 89.875 kJ/kg]
14. A boiler produces steam from water at 35°C. The enthalpy of steam is 2675 kJ/kg. Calculate the heat transferred per kg. Specific heat capacity of water is 4.19 kJ/kg. Neglect the potential and kinetic energies.
[Ans:- Q = 1384.48 kJ/kg]
15. A steam expands through an insulated nozzle following a reversible adiabatic law pVr = C. The pressure drops from 18 bar to 1.75 bar and specific volume increases from 0.045 m3 to 0.35 m3. If the inlet velocity is 76 m/s, determine the exit velocity.
[Ans:- C2 = 212.78 m/s]
16. In a steady flow of air through a nozzle, the enthalpy decreases by 50 kJ between two sections. Assuming that there are no other energy changes than the kinetic energy, determine the increase in velocity at section 2 if the initial velocity is 90 m/s.
[Ans:- C2 - C1 = 238.78 m/s]
17. 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 m3/kg and leaving at 4.5 m/s with a pressure of 6.9 bar and a specific volume of 0.16 m3/kg. The internal energy of air leaving is 88 kJ/kg greater than air entering. Cooling water in a jacket surrounding the cylinder absorbs heat from the air at the rate of 59 W. Calculate the power required to drive the compressor, and the inlet and outlet cross-sectional area.
[Ans:- Work input, W = -104.36 kW and = D1/ D2 = 1.996]
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