Explanation:

Steady flow process is a process where: the fluid properties can change from point to point in the control volume but remains the same at any fixed point during the whole process. A steady-flow process is characterized by the following:

• No properties within the control volume change with time. That is m_cv = constant; E_cv = constant
• No properties change at the boundaries with time. Thus, the fluid properties at an inlet or exit will remain the same during the whole process.
• The heat and work interactions between a steady-flow system and its surroundings do not change with time.

Concept:

Air compressor:

An air compressor is a device in which work is done on the air to raise its pressure with an appreciable increase in its density.

i.e ρ₂ > ρ₁

Volume flow rate  \((\dot{Q})\)

It is defined as the quantity of fluid (m³) flowing per second through a section. It is given by –

\(\dot{Q}=A\times{V}\)

where A = area of cross-section and V = velocity at that section.

Conservation of Mass:

For a flowing fluid, the quantity of fluid (kg) per second is constant which is given by-

\(\dot{m}=ρ_{1}A_1{V_1}=ρ_{2}A_2{V_2}\)

\(\dot{m}=ρ_{1}Q_1=ρ_{2}Q_2\)

\(∴\frac{Q_2}{Q_1}=\frac{ρ_1}{ρ_2}\)

∵ ρ₂ > ρ₁, ∴ Q₂ < Q₁ i.e. volume flow rate at the outlet decreases in case of a compressor.

Explanation:

Energy interaction for a closed system with its surrounding can take place in two ways: (i) by work transfer (ii) by heat transfer

Work and heat are modes of energy transfer.

Heat is energy transferred due to temperature differences only.

Work is the energy transfer associated with a force acting through a distance.

Relationship between heat and work:

• Both are recognized at the boundaries of a system as they cross the boundaries; That is, both heat and water are boundary phenomena
• Systems possess energy, but not heat or work
• Both are associated with a process, not a state; Unlike properties, heat or work has no meaning at a state
• Heat and work, both are path functions; Their magnitude depends on the path followed during a process as well as the end state

Explanation:

Steady flow energy equation:

\({h_1} + \frac{{v_1^2}}{2} + {z_1}g + Q = {h_2} + v_2^2 + {z_2}g + w\)

According to given condition:

Q = 0, v₁ = v₂, z₁ = z₂

And for throttling process: W = 0

h₁ = h₂

Since the enthalpy of an ideal gas is a function of temperature alone

T₁ = T₂ (For ideal gas)

The enthalpy of a real gas is not a function of temperature alone

Concept:

The steady flow energy equation is written below:

\({h_1} + \frac{{V_1^2}}{2} + {Z_1}g + \frac{{dQ}}{{dm}} = {h_2} + \frac{{V_2^2}}{2} + {Z_2}g + \frac{{dW}}{{dm}}\)

where enthalpy, heat and work are in J/kg.

Calculation:

Given: 

δQ = 0, δW = 0, Z₁ = Z₂, (h₁ - h₂) = 1.25 kJ/kg = 1.25 × 1000 J/kg

\({h_1} + \frac{{V_1^2}}{2} = {h_2} + \frac{{V_2^2}}{2}\)

K.E₁ =0 ⇒ V₁ = 0

\(\therefore ({h_1} - {h_2}) = \frac{{V_2^2}}{2}\)

\(\therefore {V_2} = \sqrt {2\left( {{h_1} - {h_2}} \right)} = \sqrt {2 × 1000\;\times\;1.25 } = 50\;m/s\)

Explanation:

Multistage compression:

An increase in pressure ratio in a single stage reciprocating compressor causes an increase in temperature, a decrease in volumetric efficiency, and an increase in work input.

So for the same higher pressure ratio, multistage compression is efficient.

Intercooling

• In multistage compression with intercooling, where the gas is compressed in stages and cooled between each stage by passing it through a heat exchanger called an intercooler. 
• Ideally, the cooling process takes place at constant pressure, and the gas is cooled to the initial temperature T1 at each intercooler.
• Multistage compression with intercooling is especially attractive when gas is to be compressed to very high pressures.
• P-V and T-S diagram of the compression with intercooling is shown in the figure below:

• It can be seen that intercooling is done at constant pressure and is represented by a horizontal line on the P-V diagram. 
• If an intercooler is installed between cylinders, in which the compressed air is cooled between cylinders, then the final delivery temperature is reduced.
• This reduction in temperature means a reduction in internal energy of the delivered air, and since this energy must have come from the input energy required to drive the machine, this results in a decrease in input work requirement for a given mass of delivered air.
• By multi staging, the pressure ratio of each stage is lowered. Thus, the air leakage past the piston in the cylinder is also reduced.
• The low-pressure ratio in a cylinder improves volumetric efficiency.

Explanation:

Heat engine and its thermal efficiency:

Work (W) is high-grade energy that can be converted into heat (Q) as low-grade energy completely, but converting heat, a low-grade energy (Q) into work, high-grade energy (W) requires special devices which are known as heat engine.

The function of a heat engine is to produce work (W_net) continuously at the expense of heat input (Q₁) to it.

The fraction of heat input (Q₁) that is converted to net-work output (W_net) is a measure of performance of a heat engine and is called thermal efficiency.

Q₁ is the heat taken from the source (T_H) and Q₂ is the heat transferred to the sink (T_L).

Net-work done by the engine, W_net = Q₁ - Q₂.

Thermal efficiency of heat engine:

\(\eta_{thermal} = \frac{work~output}{heat~input}=\frac{W}{Q_1}\Rightarrow \frac{{Q_1}\;-\;{Q_2}}{Q_1}=1-\frac{Q_2}{Q_1}\)

The ratio of brake power and indicated power is known as mechanical efficiency.

\({\eta _{mech}} = \frac{{BP}}{{IP}}\)

Concept:

The non-flow work done by the system (only on the quasi-static process) is given by:

\({W_{non - flow}} = \mathop \smallint \limits_1^2 pdV\)

Work done in a flow process (any process):

\({W_{flow - process}} = - \mathop \smallint \limits_1^2 VdP\)

Explanation:

• Based on the thermodynamic concepts, an energy source can be called as high - grade or low - grade, depending on the ease with which it can be converted into other forms.
• Thus electrical energy (or work) is called a high - grade energy, as it is very easy to convert almost all of it into other energy forms such as thermal energy (say by using an electrical heater).
• Whereas, it is not possible to convert thermal energy (or heat) completely into electrical energy (typical efficiencies of thermal power plants are around 30 percent), hence thermal energy is called a low - grade energy. 

Explanation:

Heat and work, both are path functions; Their magnitude depends on the path followed during a process as well as the end state.

• Work and heat are modes of energy transfer.
• Heat is energy transferred due to temperature differences only.
• Work is the energy transfer associated with a force acting through a distance.

Relationship between heat and work:

• Both are recognized at the boundaries of a system as they cross the boundaries; That is, both heat and work are boundary phenomena
• Systems possess energy, but not heat or work
• Both are associated with a process, not a state; Unlike properties, heat or work has no meaning at a state

Properties are classified into two types.

• Intensive property: The properties of the system which are independent of the mass of a system are called Intensive property.
  • E.g. pressure, density, temperature, all specific properties, etc.
• Extensive property: The properties of the system which are dependent on the mass of a system are called Extensive property.
  • E.g. energy, volume, entropy, etc.