Problems on Thermodynamics.

Posted on February 16, 2015 by admin Leave a comment

Problems:

1. Gas from a bottle of compressed helium is used to inflate a balloon originally folded completely flat, to a volume of 0.25 m3. If the barometer reads 760 mm of mercury, how much work is done by the system comprising the helium initially in the bottle, if the balloon is light and requires no stretching. Sketch the system before and after the process.

Solution:

The firm line S1 shows the boundary of the system before the process, and the dotted line S2 shows the boundary after the process.

Total displacement work is given by

2. Determine the work done by the air which enters an evacuated bottle from the atmosphere when the cork is opened, atmospheric air rushes into it. If the atmospheric pressure is

101.396 kPa and 0.6m3 of air (measured at atmosphere conditions) enters the bottle. Solution:

No work is done by the part of the boundary in contact with the bottle. Work is done only by the moving part external to the bottle. The pressure over this moving part is uniform at 101.396 kPa

Displacement work done by the system,

Negative, because the boundary is contracting. Thus the surroundings do positive work at the boundary and the work done by the air negative

3. A spherical balloon has a diameter of 25 cm and contains air at a pressure of 1.5 x 105Pa. The diameter of the balloon increases to 30 cm in a certain process and during this process the pressure is proportional to the diameter. Calculate the work done by the air inside the balloon during this process.

Solution:

Positive sign indicates that work is done by the system.

4. Gas from a bottle of compressed helium is used to inflate an inelastic flexible balloon, originally folded completely flat to a volume of 0.5 m3. If the barometer reads 760 mm of Hg, what is the amount of work done upon the atmosphere by the balloon (50.66 kJ)

5. When the valve of the evacuated bottle is opened, atmosphere air rushes into it. If the atmosphere pressure is 101.325 KPa, and 1.2 m3 of air (measured at atmosphere conditions) enters the bottle, calculate the work done by the air (-60.8 kJ).

6. A gas system, confined by a piston and cylinder, undergoes a change of state such that the product of pressure and volume remains constant. If the process begins at a pressure of 3 bar and a volume 0.015m3 and proceeds until the pressure falls to half its initial value, determine the magnitude and direction of the work flow.

Solution:

7. A certain amount of gas is compressed from 1 bar and 0.1m3 to 5 bar and 0.03m3. The process is according to the law pVn = K. Determine the magnitude and direction of work.

Solution: Given: p1 = 1 bar; V1 = 0.1 m3; p2 = 5 bar; V2 = 0.03 We have for a polytropic process,

8. A gas confined in a cylinder by a piston is at pressure of 3 bar and a volume of 0.015 m3. The final pressure is 1.5 bar. Determine the magnitude and direction of work transfer for the

-ve sign indicates that work is done on the system

9. A non-flow reversible process occurs for which p = 3V2 + 1/V where p is in N/cm2 and V is in m3. What is the work done when V changes from 0.5 m2 to 1 m3.

10. A system consists of a cylinder and piston machine. The external normal load applied to the piston is given by F = – 7000 + 15000L Newton’s, where L is the distance in mts from the closed and of the cylinder to the piston. How much work is done when the piston moves from the position L = 1m to L = 1.5 m. Sketch the p-V diagram for this process and show the work done.

11. An insulated system contains a mixture of ice and water. A paddle wheel is rotated in the system at 100rpm. Torque applied to the shaft is 3 N-m. In order to effect the transformation of 1 kg of ice to liquid water 300 kJ of heat must be transferred to the system. Determine the length of time the paddle wheel must be rotated in order to achieve 2.5 kg reduction in the quantity of ice.

Solution: Given: T = 3 N-m ; N = 1000 rpm

12. A system containing 5 kg of a substance is stirred with a torque of 1 N-m at a speed of 500 rpm for 24 hrs. The system mean while expands from 1.5m3 to 2.0m3 against a constant pressure of 5 bar. Determine the magnitude and direction of net work transfer.

Solution: The system is associated with two interactions with the surroundings i.e., stirring work (surroundings to the system) and displacement work

13. A mass of 1.5 kg of a substance is compressed in a quasi-static process from 0.1 MPa to 0.7 MPa. The initial pressure density of the substance is 1.16 kg/m3. Determine the magnitude of work done on the substance if i) process is pV = C and pV1-4 = C

14. O2 is compressed in a quasi static process according to the relation pV1-2 = C. The initial conditions are 98 KPa and 200 C and the final pressure is 1000 KPa. Assuming an ideal gas behaviour, determine the work required to compress 100 kg of O2. Compare this work with the work of isothermal compression, i.e., pV = C.

Solution: p1 =98 x 103 Pa, T1 = 2930 K, p2 = 1000 x 103Pa, m = 100 kg We have for polytropic process,

15. The following data refer to a12 Cylinder, single-acting, two-stroke marine Diesel engine: Cylinder diameter-0.8m

Stroke of piston-1.2m

Area of indicator diagram-5.5E10^-4 m²

Length of diagram-0.06m

Spring value-147 MPa per m

Find the net rate of work transfer from the gas to the piston in kW.

Solution: Mean effective pressure, Pm, is given by

One engine cycle is completed in two strokes of the piston or one revolution of the crank shaft.

Work done in one minute= Pm LAN

Since the engine is single-acting, and it has 12 cylinders, each contributing an equal power, the rate of work transfer from the gas to the piston is given by

16. A gas system has mass m, occupies a volume V at a pressure of p and temperature T. These properties are related by the equation where a, b and R are constants. Obtain an expression for the displacement work done by this gas system during a constant temperature process where the gas expands from 1 m3 to 10 m3 at a temperature of 293 K. Assume a = 15.7 x 104 Nm4, b = 1.07 x 10-2 and R = 0.278kJ/kg-K.