1. Months have gone by, and a particularly motivated thermodynamics student begi
ID: 1660404 • Letter: 1
Question
1. Months have gone by, and a particularly motivated thermodynamics student begins to miss piston-oylinder device problems dearly. He is worried that his newly-forged analysis skills will dull with disuse, and resoves to stay in cognitive shape. To that end, he fills a perfectly insulated piston-cylinder device with an ideal gas at high pressure and ambient (room) temperature, using locks on the piston to keep it in place. Now, he removes the locks and allows the pliston to move upwards against ambient atmosphere to a stopper What happens to the temperature of the ideal gas inside the piston-cy inder device? (a) Increases (b) Decreases Remains the same Needs more information (d) 2. An ideal gas flows steadily through the piping system and valve shown below. The inlet pressure and temperature are n and Ta and the pressure drops through the valve to a lower value, 2 Assuming the vave is well Insulated and inlet and outes pipes connected to the valve are the same diameter what is the relationship of the outlet temperature T, to the inlet temperature T,? (d) Cant tell without knowing the type of gas 3. Gas flows through a truncated cone at steady-state and constant density. The diameter at the outiet is half the diameter of the inlet The kinetic energy ofthe gas exiting is the kinetic energy of the gas entering (a) Half (b) The same as (c) Two times greater than (d) Tour times greater than (e) Sixteen times greater than 1/2Explanation / Answer
1) (d) Needs more information
From gas equation PV = nRT ; we have pressure dropping and volume increasing , but to know the Temperature change we need by what amounts or fractions are pressure and volume changing.
2) (c) T2 < T1
Because the diameter of the valve is same on both sides, the volume of the gas is not changing. At constant volume Pressure is directly proportional to Temprerature. So as pressure drops temperature also drops.
3) (e) Sixteen times greater
Because the diameter is half, the area becomes one-fourth. So from the equation of continuity i.e area is indirectly proprtional to velocity, the velocity becomes 4 times that of the initial velocity. So the Kinetic energy becomes 16 times.
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