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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?

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.

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

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.

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.

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.

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.