Thermodynamic Essay

2387 Words Nov 18th, 2014 10 Pages
Unit Two Homework Solutions, September 9, 2010
1 A frictionless piston-cylinder device initially contains 200 L of saturated liquid refrigerant-134a. The piston is free to move, and its mass is such that it maintains a pressure of 900 kPa on the refrigerant. The refrigerant is now heated until its temperature rises to 70oC. Calculate the work done during this process.
The freely-moving piston can be interpreted as giving a constant pressure process such that P1 = P2 = P = 900 kPa. For a constant pressure process, the concept that the work is the area under the path is particularly simple. That area is a rectangle whose area is P (V2 – V1). We know that P is 900 kPa, and the initial volume is 200 L = 0.2 m3, but we have to find the
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If we assume that air is an ideal gas, we can write the ideal-gas equation of state, at a constant temperature, as follows: Since mRT is a constant in a constant temperature process, we can write the equation for work as follows. We can find the ratio, V2/V1 as follows for the constant temperature process. Substituting P1/P2 in place of V2/V1, using the gas constant for air = 0.2870 kJ/(kg•K) from Table A-1 on page 908, and using the given values of m = 2.4 kg, and T = 12oC = 285.15 K, gives the following result for the work. –272 kJ
The negative sign for the work indicates that this is a work input of 272 kJ
3 A frictionless piston–cylinder device contains 2 kg of nitrogen at 100 kPa and 300 K. Nitrogen is now compressed slowly according to the relation PV1.4 = constant until it reaches a final temperature of 360 K. Calculate the work done during this process.
In this case the path equation is PVn = C with n = 1.4. We can rewrite this equation as P = CV-n, and integrate this revised path equation to find the work as follows. To reduce this equation further we can use a trick. Since PVn = C, the constant C may be written either as P1V1n or as P2V2n. By carefully choosing which way we write this constant, we can simplify our result. The equation above is valid for any substance. For an ideal gas, we can obtain a simpler result for the work by using the ideal gas equation of state, writing each PkVk product as

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