please help me with this problem,the solution of each part should be a) 15MJ b)
ID: 2280857 • Letter: P
Question
please help me with this problem,the solution of each part should be
a) 15MJ b) 20kg c) 470KJ d) 78KW,0.03
the data should come from the graph
please show me all the details,thank you so much
The first working steam engine with a piston was constructed by Thomas Newcomen between 1705 and 1711 (Jones 1970). Newcomment's engines were amazingly successful, some remaining in use for over 100 years. Most were used for pumping water, particularly for draining mines. Figure 5.7 shows a sketch of a Newcomen engine. The cylinder was first filled with steam from the boiler. During this process the weight of the piston was supported by the cross-beam, balanced by the weight of the pump side. Hence the steam pressure was essentially atmospheric and no useful work was done. At the top of the stroke cold water was admitted to the cylinder, thus creating a partial vacuum. In this process, the power stroke, the piston was forced back into the cylinder by the external pressure of the atmosphere. Excess water drained from the cylinder to the condensate cistern and subsequently fresh steam was admitted to the cylinder to begin the cycle again. The following example is based on Newcommen's later engines which were quite large. The cylinder diameter is 2 m and the working stroke of the piston is 3 m. Take the total length of the cylinder when the piston is at its maximum height to be 3.1 m. Cold water is supplied to the steam generator at 10 degreeC at atmospheric pressure, 100kpa. Calculate the mass of steam required to fill the cylinder at 100 degreeC at a pressure of 100 kpa. Determine the corresponding heat input to the steam generator. Water initially at 10 degreeC, is admitted to the cylinder until the pressure drops to 50 kpa. Assume the piston does not move significantly in this process and ignore heat transfer to the walls. Determine the amount of water required to achieve this result. (In practice the heat capacity of the walls was significant.) In the subsequent power stroke, the piston drops by 3 m. Assume this takes place quasistatically at constant pressure and determine the external work done. The engine executes ten strokes per minute. What is the average rate of work output? Obtain an approximate value for the rate of working as a fraction of the rate of heat input to the steam generator. (Ignore the work required to pump the cooling water into and out of the cylinder.)Explanation / Answer
(a) We can see from the above steam table that at 100 degree celsius and 100kPa,
Specific volume is around = 1.6 m^3 / Kg
Specific internal energy = 2.54 MJ/Kg
Volume of cylinder = pi * (1)^2 * 3 = 9.424 m^3
Mass of steam = volume/specific volume = 9.424 / 1.6 = 5.89 Kg
Heat input = mass * internal energy = 5.89*2.54 = 14.96 MJ (15MJ approx.)
(b) At 50 kPa internal energy is around 1.25 MJ/Kg
heat to extract = m*(h1-h2) = 5.89*(2.54-1.25) = 7.598 MJ
7598000 = m(water) * 4200 * 90 (Q = mc*delta(t))
m(water) = 20.10 Kg
(c) Net pressure on piston = 100 - 50 = 50kPa
Work = pressure*area*distance = 50*10^3 * pi * 3 = 471238.8 Joules
= 471 kJ
(d) Ten strokes per minute = 0.1666 strokes per second
Rate of work input i.e. power = 471*0.1666 = 78.5kW
Heat input = 15 MJ per stroke
= 15 * 0.1666 = 2.5 MJ per second
= 2500 kJ per second (kW)
Ratio = 78.5 / 2500 = 0.031
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