PROBLEMS
1. A compressed air cylinder containing air at a pressure of 3 bar, is used to fill air in balloons. Determine the work done by the air entering a big balloon till it has a volume of 100 liters. Given the balloon is light and requires no stretching. Take atmospheric pressure as 1.013 bar.
2. An engine continuously working in a cyclic process has two work transfers and three heat-transfers. The heat transfers are : 150 kJ to the working fluid, 100kJ from the working fluid, and 75 kJ to the working fluid. One of the work transfers is 150 kJ from the working fluid. What is the other work transfer?
3. During a machining process on a lathe, a workpiece of 25 cm diameter is being cut with a tool. The workpiece rotates at 300 rpm and the cutting force (tangential) is 200N. As the work piece heats up it loses heat to the surroundings. During 10 minutes of the machining process this heat loss is 60 kJ. Estimate the increase in energy of the workpiece during this process.
4. Determine whether the heat and work transfers are positive, negative or zero in the following processes undergone by the system indicated in bold letters.
(a) A pressure cooker containing hot water at 1000C is left on the cooking range with gas switched off. Kitchen temperature: 250C.
(b) A mixture
of ice and water contained in a vertical piston-cylinder arrangement with
conducting walls. Some ice melts and the piston is allowed to move to keep the
mixture pressure constant.
(c) A CNG
cylinder is connected through a valve to an evacuated vessel, all the equipment
being well insulated. The valve is opened and after some time, conditions
throughout the two vessels become uniform.
(d) Same as (b)
but walls are non-conducting and the piston is held stationary. To melt ice, a
flame is applied to the base of the cylinder which is conducting.
(e) The
safety valve of a compressed air cylinder blows off, throwing air into
the atmosphere.
5. A student keeps the doors of his refrigerator open, in order to cool her hostel room while she is away in the college. If, the temperature of the room is 250C when she leaves for college, what will the room temperature when she returns after 8 hours? Given the refrigerator has a refrigeration capacity of 500W and a COP of 2.
The change in energy of room air is related to temperature change by equation DE = 25 DT kJ
Assume there is no heat transfer from the room to the surroundings during this period.
6. A piston-cylinder arrangement contains 2l of an ideal gas at 5 bar. The piston stops are removed and the weights over it reduced so that the external pressure reduces to 2 bar and the gas expands to a volume of 5l. During this process a heat transfer of 100 J into the cylinder also takes place. What is the change in the energy of the gas?
7. A steel bar of 5mm diameter and 1m length has an initial
tensile stress of 2*105 kN/m2 . A 20 kg weights suddenly
added to the pan containing the weights pulling the bar, thus stretching the
bar further . Estimate the work done in
this process on the steel bar. Given Young’s
Modulus of steel at prevailing temperature is 2*108 kn/m2
8. A paramagnetic salt is being magnetized isothermally at 4 K to raise its magnetic moment from 100amp-m2 to 500 amp-m2. If, at the end of the process, its energy remains the same, estimate the heat transfer. Given the Salt obeys Currie’s law
M = Cc H / T with Cc = 1.3 * 10(-4) m3K
9. A battery having an emf of 10V is connected to a charger at 13V. During half an hour of charging process, 3000 Coulombs of charge is added and the battery loss 5kJ of heat to the surroundings. What is the increase in its energy?
10. A compressible fluid contained in a piston-cylinder arrangement expands when heated, its pressure and volume changing according to the relationship P=aV+b (a and b being constants) from an initial state of 4 bar pressure and 0.1m3 volume to 3 bar pressure and 0.2m3 volume. The energy of the gas is given by the equation
U= PV + 10000 J
What is the heat transfer during the process?