Exercise 2. Let X be a discrete random variable with the cumulative distribution function 0 x<1 F(x)= 0.5 1≤x<3 1 x≥
3 (1) Calculate the probability P {X ≤ 3} (2) Calculate the probability P {1 ≤ X ≤ 2}
1 answer:
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Answer:
a) the amount of energy produced in kJ/K is 0.73145 kJ/K
b) the amount of energy produced in kJ/K is 0.68975 kJ/K
The value for entropy production obtained using constant specific heats is approximately 6% higher than the value obtained when accounting explicitly for the variation in specific heats.
Explanation:
Draw the T-s diagram.
a)
= 0.939 kJ/kg.K , m = 5 kg , T₂ = 520 K , T₁ = 280
R = [8.314 kJ / 44.01 kg.K] , P₂ = 20 bar , P₁ = 2 bar
Δs =
Substitute all parameters in the equation
Δs =
Δs = 5 kg × 0.14629 kJ/kg.K
= 0.73145 kJ/K
b)
Δs =
Where T₁ = 280 K , s°(T₁) = 211.376 kJ/kmol.K
T₂ = 520 K , s°(T₂) = 236.575 kJ/kmol.K
R = [8.314 kJ / 44.01 kg.K] , M = 44.01 kg.K , P₂ = 20 bar , P₁ = 2 bar
Δs =
= 5 kg (0.13795 kJ/kg.K)
= 0.68975 kJ/K
The value for entropy production obtained using constant specific heats is approximately 6% higher than the value obtained when accounting explicitly for the variation in specific heats.