Reference no: EM132406932

Advanced Thermodynamics Problems -

1. Maximum Available (Minimum Required) Work

1.1. The air having pressure p₁ = 0.1 MPa and temperature T₁ = 20^oC flows into the compressor with velocity w₁ = 1m/s. It is compressed to the pressure of p₂ = 1 MPa. Find the minimum power of an engine running the compressor if the claimed mass rate of flow of the air is equal to m^· = 3.0 · 10^-4 kg/s. Assume that the compressor is thermally insulated and that the inlet and outlet areas of cross-section are equal. The air may be treated as an ideal diatomic gas of the particular gas constant R = 287 kJ/(kg · K).

1.2. The pneumatic engine is fed with an air of pressure p₁ = 1 MPa and temperature T1 = 20^oC. Find the maximum power of the engine (in steady state) if the exit pressure is equal p₂ = 0.1 MPa. The mass rate of the air flow is equal to m^· = 3.0 · 10^-3 kg/s. Assume that the engine is thermally insulated and that influence of difference in the inlet and outlet air velocity is negligible. The air may be treated as an ideal two-atomic gas of the particular gas constant R = 287 kJ/(kg · K).

1.3. A container has been divided into parts (A and B) and filled with an ideal gas the isentropic constant equal to κ = 1.5. Initial properties of the gas in two parts of the container are equal to: p_A = 1 MPa, T_A = 800 K, V_A = 0.03 m³ and p_B = 0.2 MPa, T_B = 400K, V_A = 0.06m³, respectively. Find the maximum work that can be extracted from difference in properties of two parts of the container.

2. EXERGY (Availability)

2.1. The air flows out a motionless nozzle to the environment. Air pressure, temperature and the exit velocity are equal to p₁ = 2 MPa, T₁ = 20^oC, velocity w = 100 m/s, respectively. The exit diameter of the nozzle is d = 20 cm. Air pressure and temperature in the environment amounts p_e = 0.1 MPa, T_e = 20^oC. Find exergy loss of the air leaving the nozzle assuming that its expansion is isothermal. The air may be treated as an ideal diatomic gas of the particular gas constant R = 287 kJ/(kg · K).

2.2. Find exergy loss of an air stream having temperature T₁ = 298 K, which has flown through the perpendicular shock wave. Ratio of pressures (after and before the shock wave) is equal to p₂/p₁ = 10.

2.3. The air with pressure p₁ = 2 MPa is feeding a facility, which operation needs sustaining of constant gas pressure of p₂ = 0.2 MPa. Pressure decrease is carried out in the throttling valve. Find exergy loss per unit mass of the air in the if the environmental temperature is equal to T_e = T₂ = 25^oC. Assume that the valve is thermally insulated.

2.4. Compressed air with initial properties: p₁ = 0.35 MPa, T₁ = 30^oC is adiabatically and irreversibly expanded in a pneumatic engine. The air leaving the engine has pressure p₂ = 0.1 MPa and temperature T₁ = -35^oC. The mass rate of air flowing through the engine is equal to n^· = 1.0 · 10^-3 kmols/s. Find exergy loss of the air per unit time the if the environmental temperature and pressure are p_e = 0.1 MPa, T_e = 10^oC.

2.5. The air enters a wind tunnel of the internal diameter equal to D = 2m and flows around an aircraft model. The mean air pressure and velocity in the tunnel in front of the model are, p₁ = 0.15 MPa, w₁ = 100 m/s respectively. The mean pressure far behind the model equals p₂ = 0.10 MPa. Find the aerodynamic force acting on the model assuming that variation in pressure along the empty tunnel is negligible and the tunnel is thermally insulated. Neglect variation in temperature of the air and assume that the environmental temperature equals T_e = 25^oC.

2.6. A heat pump is used to heat up a flowing gas. The molar flow rate of the heated gas is n^· = 0.01 kmol/s while its molar heat capacity (Mc_p)_g = 30.56 kJ/(kmol · K). The heat pump utilises the air as the working medium. The air in the pump cycle is isentropically compressed (pressure ratio p₂/p₁ = 8). Its temperature varies from T₁ = 273 K to T₃ = 353 K behind the first heat exchanger where the air isobarically delivers heat to the heated gas. The heated gas changes its temperature from T_a = 338 K to T_b = T₂ - 25K. The working medium is isentropically decompressed and then flows through the second heat exchanger where it isobarically absorbs heat from the environment. Finally, the air enters the compressor again thus closing the cycle. The environmental temperature equals T_e = 283 K. Find: a) power delivered to the decompressing device; b) loss of exergy in the cycle; c) the second law efficiency of the heat pump.

2.7. A refrigerator runs according to the Carnot cycle. The working medium absorbs heat in the evaporator having the constant temperature T₁ = 255 K and gives it over in the condenser having the constant temperature T_II = 300 K. Temperature of the working medium in the evaporator is 10 K lower than the evaporator temperature while temperature of the working medium in the condenser is higher by 10 K than the condenser temperature. Find the second law efficiency of the refrigerator.

2.8. Air (two-atomic ideal gas) with a particular gas constant R = 287 J/(kg · K) flows out of a divergent nozzle (with the outlet diameter d = 20 cm do the surroundings. Air pressure and temperature in nozzle before leaving it are p₁ = 2 MPa and T₁ = 20oC, respectively. The air velocity at the nozzle outlet is w₁ = 100 m/s. Find the exergy loss of the air leaving the nozzle assuming that the process of decompression is isothermal. The air pressure and temperature in the surroundings are p_e = 0.1 MPa and T_e = 20^oC, respectively.

2.9. The air having inlet properties: p₁ = 0.5 MPa, T₁ = T_e = 20^oC, flows through a long, horizontal, well thermally insulated tube. The tube diameter is equal to d = 40 mm. The outlet temperature and pressure of the air are, p₂ = 0.2 MPa, T₂ = 30^oC, respectively. Find the exergy loss per unit mass of the air. The mass rate of the air is m^· = 0.2 kg/s and the particular gas constant of the air R = 287 J/(kg · K). Estimate the loss of exergy in the case when the air in the tube would be well cooled and its temperature would not vary along the duct.

2.10. A hot-water stream at T₁ = 70^oC enters an adiabatic mixing chamber with a mass flow rate of m^·₁ = 2 kg/s, where it is mixed with a stream of cold water at T₂ = 20^oC. If the mixture leaves the chamber at T₃ = 45^oC, determine: a) the mass flow rate of the cold water, b) the exergy loss per unit time during this adiabatic mixing process. Assume that all streams are at a pressure p₁ = p₂ = p₃ = 0.35 MPa and the environmental temperature is T_e = 10^oC. The specific heat of liquid water is c_w = 4.19 kJ/(kg · K).