Solution :
Given :
The number of blows is given as :
0 - 6 inch = 4 blows
6 - 12 inch = 6 blows
12 - 18 inch = 6 blows
The vertical effective stress 


Now,

corrected N - value of overburden
effective stress at level of test
0 - 6 inch, 
= 9.86
6 - 12 inch, 
= 14.8
12 - 18 inch, 
= 14.8

= 13.14
= 13
Answer:
A) β_max = 20.64
B) TH = 68.25°C
C) TC = 54.27°C
Explanation:
A) We are given;
TH = 16°C = 16 + 273K = 289K
TC = 2°C = 2 + 273K = 275K
Formula for maximum cycle coefficient of performance is given as;
β_max = TH/(TH - TC)
β_max = 289/(288 - 275)
β_max = 20.64
B) We are given;
Heat rejected to system at hot reservoir; Q_H = 10.5 KW
Heat provided to system at cold reservoir; Q_C = 8.75 KW
Cold reservoir temperature; TC = 0°C = 0 + 273K = 273K
Formula for actual cycle COP is given as;
β_actual = Q_C/W_cycle
Where W_cycle is the work done and is given by;
W_cycle = Q_H - Q_C
W_cycle = 10.5 - 8.75 = 1.75 KW
Thus,
β_actual = 8.75/1.75
β_actual = 5
Actual cycle COP is defined as;
β_actual = TH/(TH - TC)
And we are looking for TH.
Thus,
TH = TC/(1 - (1/β_actual))
TH = 273/(1 - 1/5)
TH = 273/(4/5)
TH = 341.25K = 341.25 - 273°C = 68.25°C
C) We are given;
TH = 27°C = 27 + 273 = 300°C
β_max = 12
Thus, from,
β_max = TH/(TH - TC)
TC = TH(1 - (1/β_max))
TC = 300/(1 - 1/12)
TC = 327.27K = 327.27 - 273 °C = 54.27°C
Answer:
a) 0.27 % b) 0.27%
Explanation:
a) The inspector can choose 1 part from 11 parts in 11C1 ways. These are total number of mutually exclusive events.
Now three cavities are effected by temperature Malfunction that results in the parts that do not conform to specifications. To obtain exactly 1 non conforming part the inspector have to choose from one of the three cavities that are effected by temperature. This can be done in 3C1 ways.
Probability that inspector finds out exactly 1 non conforming part is,
Probability =
Probability =
= 3 / 11
= 0.27 %
b) As the inspector is choosing only 1 part for inspection so the probability to find exactly 1 non conforming part is same as the probability to find at least 1 non conforming part.
So the probability is 0.27 %.