A civil engineer is studying a left-turn lane that is long enough to hold seven cars. Let X be the number of cars in the line at
the end of a randomly chosen red light. The engineer believes that the probability that X = x is proportional to (x + 1)(8 − x) for x = 0, . . . , 7 (the possible values of X), i.e. P(X = x) = ( C(x + 1)(8 − x) for x = 0, 1, . . . , 7 0 otherwise 1. Determine the value of C. 2. Find the probability that X will be at least 5.
2 answers:
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Answer:
a. which is constant therefore, n = constant
b. The temperature at the end of the process is 109.6°C
c. The work done by the balloon boundaries = 10.81 MJ
The work done on the surrounding atmospheric air = 10.6 MJ
Explanation:
p₁ = 100 kPa
T₁ = 27°C
D₁ = 10 m
v₂ = 1.2 × v₁
p ∝ α·D
α = Constant
v₂ = 1.2 × v₁ = 1.2 × 523.6 = 628.32 m³
Therefore, D₂ = 10.63 m
We check the following relation for a polytropic process;
We have;
n = -1/3
Therefore, the relation, pVⁿ = Constant
b. The temperature T₂ is found as follows;
T₂ = 300.15/0.784 = 382.75 K = 109.6°C
c.
p₂ = 100000/0.941 = 106.265 kPa
The work done by the balloon boundaries = 10.81 MJ
Work done against atmospheric pressure, Pₐ, is given by the relation;
Pₐ × (V₂ - V₁) = 1.01×10⁵×(628.32 - 523.6) = 10576695.3 J
The work done on the surrounding atmospheric air = 10.6 MJ