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Devise a Monte Carlo algorithm that determines whether a permutation of the integers 1 through n has already been sorted (that is, it is in increasing order), or instead, is a random permutation. A step of the algorithm should answer “true” if it determines the list is not sorted and “unknown” otherwise. After k steps, the algorithm decides that the integers are sorted if the answer is “unknown” in each step. Show that as the number of steps increases, the probability that the algorithm produces an incorrect answer is extremely small. [Hint: For each step, test whether certain elements are in the correct order. Make sure these tests are independent.]
Laboratory tests on human teeth indicate that hte area effective during chewing is approximately 0.25 cm^2 and that the tooth length is about 1.1 cm. If the applied load in the vertical direction is 880 N and the measured shortening is 0.004 cm. Determine Young's Modulus
A steel cube is subjected to a hydrostatic pressure of 1.5 MPa. Because of this pressure the volume decreases to give a dilatation of -10^-5. The Young's Modulus of the material is 200 GPa. Determine Poisson's Ratio of the material and also the bulk modulus.
Oxygen, at 200 bar is to be stored in a steel vessel at 20 OC. The capacity of the vessel is 0.04 m3.
Calculate the mass of oxygen that can be stored in the vessel. The vessel is protected against excessive pressure by a fusible plug which will melt if the temperature rises too high.
At what temperature must the plug melt to limit the pressure in the vessel to 240 bar?
Steam at 7 bar , dryness 0.9 , expands in a piston cylinder assembly at constant pressure until the temperature is 200 C . CALCULATE THE WORK DONE AND HEAT SUPPLIED PER KG OF STEAM DURING THE PROCESS
An ideal Diesel engine has a compression ratio
of 20 and uses air as the working fluid. The state of the air
at the beginning of the compression process is 95 kPa and
20oC. If the maximum temperature in the cycle is not to
exceed 2200 K, determine
• The thermal efficiency.
Use constant specific heats at room temperature.
An ideal Diesel cycle has a compression
ratio of 20 and cut off ratio of 1.3. Determine the
maximum temperature of the air and the rate of heat
addition to this cycle when it produces 250 kW of
power. The air is at 90 kPa and 15oC at the end of the
suction stroke
The compression ratio of an air-standard Otto cycle is
9.5. Prior to the isentropic compression process, the air is at 100
kPa, 35oC, and 600 cm3
. The temperature at the end of isentropic
expansion process is 800 K. Using specific heat values at room
temperature, determine (a) the highest temperature and
pressure in the cycle; (b) the amount of heat transferred; (c) the
thermal efficiency.
An ideal Otto cycle has a compression ratio of 8 and takes
in air at 95 kPa and 15oC, and the maximum cycle temperature is
1200oC. Determine the heat transferred to and rejected from this
cycle, as well as the cycle’s thermal efficiency.
An ideal Otto cycle has a compression ratio of 10.5, takes in
air at 90 kPa and 40oC, and is repeated 2500 times per minute. Using
constant specific heats at room temperature, determine the thermal
efficiency of this cycle and the rate of heat input if the cycle is to
produce 90 kW of power.
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