Chapter – 4 : JSSC JE Mechanical Notes

First Law of Thermodynamics

• First Law = Law of Conservation of Energy.
• Energy can neither be created nor destroyed; it can only be transferred or transformed.
• For a thermodynamic system: Heat supplied = Increase in stored energy + Work done.
• For a closed system: \( Q = \Delta U + W \)
• Sign convention: \( Q > 0 \) → heat supplied to system; \( W > 0 \) → work done by system.

Stored Energy

• Stored energy = Energy possessed by a system due to its state or position.
• Main forms:
  • Internal energy (\( U \)) – molecular/thermal energy stored inside the system.
  • Kinetic energy (KE) = \( \frac{mV^2}{2} \)
  • Potential energy (PE) = \( mgz \)
• Total energy of a system:\( E = U + KE + PE \)

  \( E = U + \frac{mV^2}{2} + mgz \)

Internal Energy (\( U \))

• Internal energy = Microscopic energy associated with molecular motion and molecular interactions.
• It is a property/state function.
• For a pure substance, internal energy depends on its thermodynamic state.
• \( \Delta U = U_2 – U_1 \)
• For an ideal gas, \( U = f(T) \); therefore internal energy depends only on temperature.
• Specific internal energy: \( u = U/m \)

First Law for a Cyclic Process

• In a cycle, the system returns to its initial state.
• Therefore, change in any property over one complete cycle = 0.
• Hence: \( \Delta U = 0 \)
• First law:\( \oint \delta Q = \oint \delta W \)
• Therefore, for a cyclic process:Net heat supplied = Net work done
• This law establishes conservation of energy but does not specify the direction of heat flow.

Non-Flow Energy Equation (NFEE)

• Used mainly for a closed system where there is no mass crossing the system boundary.
• General energy equation:

\( Q – W = \Delta U + \Delta KE + \Delta PE \)

• Expanded form:

\( Q – W = (U_2 – U_1) + \frac{m(V_2^2 – V_1^2)}{2} + mg(z_2 – z_1) \)

• If changes in kinetic and potential energies are negligible:

\( Q – W = \Delta U \)

• Therefore: \( Q = \Delta U + W \)

Flow Energy

• In an open system/control volume, fluid continuously enters and leaves.
• Energy required to push fluid into or out of a control volume is called Flow Energy.
• Flow energy per unit mass = \( Pv \)
• Since \( v = 1/\rho \):Flow energy = \( P/\rho \)
• For mass \( m \): Flow energy = \( mPv \)

Enthalpy (\( H \))

• Enthalpy is defined as:

\( H = U + PV \)

• Specific enthalpy:

\( h = u + Pv \)

• Enthalpy combines:Internal energy + Flow energy
• It is a property/state function.
• Unit of specific enthalpy: kJ/kg.
• For an ideal gas: \( h = h(T) \); therefore enthalpy depends only on temperature.
• Important relation:\( \Delta h = \Delta u + \Delta(Pv) \)

Steady State

• A system is in steady state when its properties at a fixed point do not change with time.
• At steady state:
  • Mass inside control volume remains constant.
  • Energy stored inside control volume remains constant.
  • No accumulation of mass or energy with time.
• For mass:Rate of mass entering = Rate of mass leaving

Steady Flow

• Steady flow means fluid properties at a particular location remain constant with time.
• Examples: turbine, compressor, pump, nozzle, boiler, condenser, heat exchanger.
• For steady flow:\( \dot{m}_1 = \dot{m}_2 \) for a single-inlet, single-outlet device.
• Mass flow rate:

\( \dot{m} = \rho A V = \frac{AV}{v} \)

Conditions for Steady-State Steady-Flow (SSSF)

• Flow properties at a fixed point remain constant with time.
• No accumulation of mass inside the control volume.
• No accumulation of energy inside the control volume.
• For one inlet and one outlet:\( \dot{m}_1 = \dot{m}_2 \)
• Heat transfer, work transfer and mass flow may occur, but their rates remain constant with time.

Steady Flow Energy Equation (SFEE)

• SFEE is the First Law applied to a steady-flow control volume.

\( \dot{Q} – \dot{W} = \dot{m}\left[(h_2 – h_1) + \frac{V_2^2 – V_1^2}{2} + g(z_2 – z_1)\right] \)

• Per unit mass:

\( q – w = (h_2 – h_1) + \frac{V_2^2 – V_1^2}{2} + g(z_2 – z_1) \)

• Using specific kinetic and potential energy:

\( q – w = \Delta h + \Delta\left(\frac{V^2}{2}\right) + \Delta(gz) \)

SFEE – Important Special Cases

Closed System vs Open System

Most Important Formulae

• Total energy: \( E = U + \frac{mV^2}{2} + mgz \)
• First law: \( Q = \Delta U + W \)
• Cyclic process: \( \oint \delta Q = \oint \delta W \)
• NFEE: \( Q – W = \Delta U + \Delta KE + \Delta PE \)
• Flow energy: \( Pv \)
• Enthalpy: \( H = U + PV \)
• Specific enthalpy: \( h = u + Pv \)
• Mass flow rate: \( \dot{m} = \rho A V \)
• SFEE: \( q – w = \Delta h + \Delta(V^2/2) + \Delta(gz) \)
• Pressure energy per unit mass: \( Pv \)

Exam Traps

• \( U \) = internal energy; \( H \) = enthalpy.
• Enthalpy = Internal energy + Flow energy.
• Flow energy per unit mass = \( Pv \).
• For a complete cycle: \( \Delta U = 0 \).
• Therefore cyclic process: Net heat = Net work.
• NFEE → mainly closed system.
• SFEE → mainly open/steady-flow system.
• Steady state → properties at a fixed location do not change with time.
• Steady flow ≠ zero flow; fluid can continuously flow while properties remain constant with time.
• For an ideal gas, both \( u \) and \( h \) depend only on temperature.

One-Minute Revision

• 1st Law → Conservation of Energy
• Closed system → \( Q – W = \Delta U + \Delta KE + \Delta PE \)
• Cycle → \( \Delta U = 0 \) → \( \oint Q = \oint W \)
• Flow energy → \( Pv \)
• Enthalpy → \( H = U + PV \)
• Specific enthalpy → \( h = u + Pv \)
• Steady state → No time variation at a fixed point
• Steady flow → Continuous flow with time-independent properties at fixed locations
• SFEE → \( q – w = \Delta h + \Delta KE + \Delta PE \)
• Turbine → produces work
• Compressor/Pump → consumes work
• Nozzle → enthalpy decreases, velocity increases