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Answer:
The plot of the function production rate m(t) (in kg/min) against time t (in min) is attached to this answer.
The production rate function M(t) is:
(1)
The Laplace transform of this function is:
(2)
Explanation:
The function of the production rate can be considered as constant functions by parts in the domain of time. To make it a continuous function, we can use the function Heaviside (as seen in equation (1)). To join all the constant functions, we consider at which time the step for each one of them appears and sum each function multiply by the function Heaviside.
For the Laplace transform we use the following rules:
(3)
(4)
Answer:
The initial temperature will be "385.1°K" as well as final will be "128.3°K".
Explanation:
The given values are:
Helium's initial volume, v₁ = 6 m³
Mass, m = 1.5 kg
Final volume, v₂ = 2 m³
Pressure, P = 200 kPa
As we know,
Work,
On putting the estimated values, we get
⇒
⇒
⇒
Now,
Gas ideal equation will be:
⇒
On putting the values. we get
⇒
⇒
⇒ (Initial temperature of helium)
and,
⇒
On putting the values, we get
⇒
⇒
⇒ (Final temperature of helium)