A piston–cylinder assembly contains air, initially at 2 bar, 300 K, and a volume of 2 m3. The air undergoes a process to a state where the pressure is 1 bar, during which the pressure–volume relationship is pV 5 constant. Assuming ideal gas behavior for the air, determine the mass of the air, in kg, and the work and heat transfer, each in kJ.

Work, W = 277.269kJ

Internal energy, Q = 277.269kJ

Explanation:

Given-

Pressure, P1 = 2 bar

Temperature, T1 = 300K

Volume, V1 = 2m³

P2 = 1 bar

PV = constant

Let,

mass in kg be m

Work in kJ be W

Heat transfer in kJ be Q

R' = 8.314 kJ/kmolK

Mass of air, Mair = 28.97 kg/kmol

R = 0.289 kJ/kgK

We know,

PV = mRT

m = 5.65kg

To calculate V₂:

PV = constant = P₁V₁ = P₂V₂

P₁V₁ = P₂V₂

V₂ = 4m³

To calculate the work:

P₁V₁ = C

P₁ = C/ V₁

where limit is V₁ to V₂

To calculate heat transfer:

Q - W = Δu

Q - W = m (u₂ - u₁)

Q = W + m (u₂ - u₁)

Q = W + m X cv X (T₂ - T₁)

Since, T₁ ≈ T₂

There is no change of internal energy.

W = Q

Q = 277.269kJ

Examples includes

Biological Examples

1. Body temperature humans -in humans the hypothalamus intercept and counters fluctuations in the body temperature

2. Blood pressure in humans; when signals of increased blood pressure are sent to the brain from the blood vessels, it responds by sending signals to the heart to slow down the rate of heart beat

Mechanical Example

1. The toilet ballcock rises in as the water level in it rises, and closing the inlet valve to turns off the water when the allowable water level is reached.

Explanation:

Negative Stabilizing Feedback

A reaction that causes a decrease in function is a negative stabilizing feedback . It is initiated as a response to a type of stimulus. It normally leads to a reduction in the system output as such, the feedback stabilises system. in biological terms, this is known as homeostatis, while in mechanics it is called equilibrium. an appraisal of person's work is also a type of negative feedback.