• Suppose that a particular algorithm has time complexity T(n) = 10 ∗ 2n, and that execution of the algorithm on a particular ma
1 answer:
Answer:
The number of inputs processed by the new machine is 64
Solution:
As per the question:
The time complexity is given by:
where
n = number of inputs
T = Time taken by the machine for 'n' inputs
Also
The new machine is 65 times faster than the one currently in use.
Let us assume that the new machine takes the same time to solve k operations.
Then
T(k) = 64 T(n)
k = 64n
Thus the new machine will process 64 inputs in the time duration T
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Assumptions:
- Steady state.
- Air as working fluid.
- Ideal gas.
- Reversible process.
- Ideal Otto Cycle.
Explanation:
Otto cycle is a thermodynamic cycle widely used in automobile engines, in which an amount of gas (air) experiences changes of pressure, temperature, volume, addition of heat, and removal of heat. The cycle is composed by (following the P-V diagram):
- Intake <em>0-1</em>: the mass of working fluid is drawn into the piston at a constant pressure.
- Adiabatic compression <em>1-2</em>: the mass of working fluid is compressed isentropically from State 1 to State 2 through compression ratio (r).
- Ignition 2-3: the volume remains constant while heat is added to the mass of gas.
- Expansion 3-4: the working fluid does work on the piston due to the high pressure within it, thus the working fluid reaches the maximum volume through the compression ratio.
- Heat Rejection 4-1: heat is removed from the working fluid as the pressure drops instantaneously.
- Exhaust 1-0: the working fluid is vented to the atmosphere.
If the system produces enough work, the automobile and its occupants will propel. On the other hand, the efficiency of the Otto Cycle is defined as follows:
where:
Ideal air is the working fluid, as stated before, for which its specific heat ratio can be considered constant.
Answer:
See image attached.
