THERMODYNAMICS, HEAT AND MASS TRANSFER TUTORIAL NO: 1 (SPECIFIC VOLUME, PRESSURE AND TEMPERATURE) 1. A vacuum gauge mounted on a condenser reads 66 cm Hg. What is the absolute pressure in the condenser in kpa when the atmospheric pressure is 101.3 kpa? Take density of mercury 13600 kg/m 3 and the local acceleration 9.81 m/s 2. 2. The 50 kg piston is free to move in the vertical cylinder and has a diameter of 12 cm. If the atmospheric pressure is equal to 0.1 MPa and the acceleration due to gravity is 9.81 m/s 2, determine the absolute pressure of H 2 O. 3. A turbine is supplied with steam at a gauge pressure of 1400 kpa. After expansion in the turbine the steam flows into a condenser, which is maintained at a vacuum of 710 mm of Hg. The barometric pressure is 772 mm of Hg. Express the inlet and exhaust absolute steam pressure in kpa. Take the density of mercury as 13600 kg/m 3. 4. Figure P 1.4 shows a tank within a tank, each containing air. Pressure gauge A is located inside the tank B and reads 140 kpa. The U-tube manometer connected to tank B contains mercury. Using data on the diagram determine the absolute pressures inside the tank A and tank B, each in bar. The atmospheric pressure surrounding tank B is 101 kpa. The acceleration of gravity is g = 9.81 m/s 2. Figure P 1.4 5. A piston-cylinder with a cross-sectional area of 0.01 m 2 has s piston mass of 100 kg resting on the stops, as shown in Figure P 1.5. With an outside atmospheric pressure of 100 kpa, what should the water pressure be to lift the piston? [R Gnyawali/P Timilsina] Page 1
Figure P 1.5 6. A vessel shown in Figure P 1.6 has two compartments at different pressures. The pressure gauge A reads 4 bar gauge and B reads 2 bar gauge. The barometer reads 760 mm of Hg. Calculate the reading of gauge C. Take density of mercury 13600 kg/m 3 and the local acceleration 9.8 m/s 2. Figure P 1.6 7. A frictionless piston cylinder device has a cross sectional area of 100 cm 2. Find the piston mass such that the absolute pressure in the cylinder is 1.0 MPa. Atmospheric pressure is 0.1 MPa and the local acceleration is 9.81 m/s 2. 8. Steam in compartments A and B are separated by a membrane, v A = 17.196 m 3 /kg, and v B = 3.418 m 3 /kg, as shown in Figure P 1.8. If the membrane is broken, find the resultant specific volume. Figure P 1.8 9. The device shown in Figure P 1.9 has a free moving piston between the two chambers. The initial total volumes of A and B are equal with v A = 100 m 3 /kg and v B = 50 m 3 /kg. If the piston is moved so that x is one-fourth of the entire length, determine the final specific volumes of chambers A and B. [R Gnyawali/P Timilsina] Page 2
Figure P 1.9 10. A new scale N of temperature is devised in such a way that the freezing point of ice is 100 0 N and boiling point is 400 0 N. What is the temperature reading on this new scale when the temperature is 150 0 C? At what temperature, both the Celsius and new temperature scale reading would be the same? 11. Attached to the containers shown in Figure P1.11 are three pressure gauges. Determine the absolute pressure in compartment 2 and reading of pressure gauge c. Figure P 1.11 12. The piston of a vertical piston cylinder device containing a gas has a mass 60 kg and a cross sectional area of 0.04 m2, as shown in Figure P1.12. The gravitational acceleration is 9.81 m/s2. A. Determine the pressure inside the cylinder. B. If some heat is transferred to the gas and its volume is doubled, do you expect the pressure inside the cylinder to change? 13. Steam in a container is separated by a membrane, as shown in Figure P1.13; the specific volume of the steam in B is 0.5951 m 3 /kg. The membrane breaks, and the resulting specific volume is 0.7964 m 3 /kg. Find the original specific volume in A. [R Gnyawali/P Timilsina] Page 3
Figure P1.12 Figure P1.13 14. A piston-cylinder assembly shown in Figure P 1.14 contains a gas at a pressure of 200 kpa. If the area of cross-section of the piston is 0.01 m 2 and the mass of the piston is 50 kg, what external atmospheric pressure P 0 is required to just keep the piston resting on the stops. Take g= 9.81 m/s 2 Figure P 1.14 15. A 5 kg piston in a cylinder with diameter of 100 mm is loaded with a spring and the outside atmospheric pressure of 100 kpa. The spring exerts no force on the piston when it is at the bottom of the cylinder and for the state shown in figure 1.15, the pressure is 400 kpa with volume of 0.4 L. The valve is opened to let some air in, causing the piston to rise 2 cm. Find the new pressure. Take g= 9.81 m/s 2 Figure P 1.15 ANSWERS: 1. 13.25 kpa 9. v A = 50 m 3 /kg, v B = 75 m 3 /kg [R Gnyawali/P Timilsina] Page 4
2. 143.37 kpa 3. 1502.997 kpa, 8.272 kpa 10. 550 o N, -50 4. 127.66 kpa, 267.66 kpa 11. 2.5 MPa, 1.5 MPa 5. 198.1 kpa 12. 112 kpa, No 6. 2 bar 13. 0.9873 m 3 /kg 7. 917.43 kg 14. 150.95 kpa 8. 4.433 m 3 /kg 15. 515.36 kpa [R Gnyawali/P Timilsina] Page 5