First Law Analysis of Cycles P M V Subbarao Professor Mechanical Engineering Department A Law of sizing for thermodynamic Equipment…..

The Thermodynamic Cycle Burn Coal (to add Heat slowly) Ability to Perform The Work (Move piston slowly) Ecological Nuisance

Conservation of Energy Energy can neither be created nor be destroyed. In a Cycle, Net work Transfer = Net Heat Transfer. This is The First Law of Thermodynamics.

Cyclic Integral of Heat transfers = Cyclic Integral of Work transfers The First Law of Cycles During Any cycle a closed system undergoes, the cyclic integral of the heat is proportional to the cyclic integral of work. Cyclic Integral of Heat transfers = Cyclic Integral of Work transfers This is a law of nature. Can be described only for closed system. Basis is only experimental evidence. The first law can never be disproved.

Carnot Model for Engine

Relating a cycle to Processes

Relating a cycle to Processes Any variable, which is independent of path (process) during a change of state is called as a property. Let this variable be E. E is having units of heat or work and is called as total energy of the system.

First law for a Closed System during a Process The change in energy of a system during a change of state is numerically equal to the algebraic sum of heat transfer during the process and the work transfer during the process. Remarks: Only change of energy has been defined. Zero Energy has to be expressed with respect to some arbitrary reference! Q and W must be measured in same units.

Further Remarks on Definition of Energy The Energy of a system at any state A is: Ea = Eref +DE. How to Define zero energy state? One popular definition: Stagnant Liquid at triple point at sea level will have zero energy. Energy is an extensive property. The energy of a system of unit mass is called as specific energy. Specific energy is an intensive property.

Members of the Family of Energy FORMS OF ENERGY All forms of energy fall under two categories Microscopic or Macroscopic and/or Potential Energy or Kinetic Energy. Potential energy is stored energy and the energy by the virtue of state or position. Macro Potential Energy : Gravitational Energy or Strain energy. Micro Potential Energy : Chemical energy and Nuclear energy. Kinetic energy is due to motion (Motive Energy) - the motion of waves, electrons, atoms, molecules and system.

Potential Energy CHEMICAL ENERGY : Chemical energy is the energy stored in the bonds of atoms and molecules. Biomass, petroleum, natural gas, propane and coal are examples of stored chemical energy. NUCLEAR ENERGY : Nuclear energy is the energy stored in the nucleus of an atom - the energy that holds the nucleus together. The energy of nucleus of a uranium and Thorium atoms is an example of nuclear energy. STORED MECHANICAL ENERGY : Stored mechanical energy is energy stored in objects by the application of a force. Compressed springs and stretched rubber bands are examples of stored mechanical energy.

Potential Energy GRAVITATIONAL ENERGY : Gravitational energy is the energy of place or position. Water in a reservoir behind a hydropower dam is an example of gravitational potential energy.

Kinetic Energy RADIANT ENERGY : Radiant energy is electromagnetic energy that travels in transverse waves. Radiant energy includes visible light, x-rays, gamma rays and radio waves. Solar energy is an example of radiant energy. THERMAL ENERGY : Thermal energy is the internal energy in substances - the vibration and movement of atoms and molecules within substances. Geothermal energy is an example of thermal energy. MOTION :The movement of objects or substances from one place to another is motion.

Kinetic Energy SOUND : Sound is the movement of energy through substances in longitudinal (compression/rarefaction) waves. ELECTRICAL ENERGY: Electrical energy is the movement of electrons. Lightning and electricity are examples of electrical energy.

Change in Energy During A Process : Closed System Q -W depends only on the initial and final states and not on the path followed between the two states. Therefore it is the differential of a property of the system. This property is the energy of the mass and is given the symbol E. Thus E = Micro Kinetic energy + Micro potential energy +Macro kinetic energy + Macro potential energy + ….. E = Internal energy +Macro kinetic energy + Macro potential energy + …..

The Energy The first law of thermodynamics for a CM during an infinitesimal process

INCOMING RESOURCE FOSSIL FUEL WINDS WIND ENERGY CLOUDS HYDRO ENERGY VEGETATION CHEMICAL ENERGY OCEAN THERMAL ENERGY SOLAR RADIATION WAVE VELOCITY RAINS CO2 + H2O PHTOSYNTHESIS SOLAR ENERGY INCOMING RESOURCE FOSSIL FUEL COAL PETROLEUM NATURAL GAS FOSSILIZATION ONE TIME SYSTEM

Of this, approximately 1-2% is converted to wind energy. The Sun provides 175 million million watts of energy to the Earth’s atmosphere each hour. Of this, approximately 1-2% is converted to wind energy.

Microscopic Energy This energy is defined as the energy associated with the random, disordered motion of molecules and due to intermolecular forces. It is separated in scale from the macroscopic ordered energy associated with moving or stationary objects; It refers to the invisible form of energy at atomic and molecular scales. Popularly known as Internal Energy, U.

Internal (Microscopic) Energy : Ideal Gas Internal energy involves energy at the microscopic scale. Potential and Kinetic energies of individual molecules/atoms. But the potential energy is associated with intermolecular forces which are presumed to be zero in an ideal gas. Therefore the internal energy of an ideal gas is entirely kinetic energy.

Internal (Microscopic) Energy : Monatomic Ideal Gas For an ideal monatomic gas, this is just the translational kinetic energy of the linear motion of the "hard sphere" type atoms. For a monatomic ideal gas this change in internal energy is given by :

Internal (Microscopic) Energy : Diatomic Ideal Gas For polyatomic gases there is rotational and vibrational kinetic energy as well.

Internal (Microscopic) Energy : Polyatomic Ideal Gas

Internal (Microscopic) Energy : Other Substances Then in real gases, liquids and solids there is potential energy associated with the intermolecular attractive forces.

Increase of Internal Energy Supply enough heat to each of these systems till the there is 1C increase in temperature.

Internal Energy and Temperature

Internal Energy of an Ideal Gas Internal energy in general includes both kinetic energy and potential energy associated with the molecular motion. But the potential energy is associated with intermolecular forces which are presumed to be zero in an ideal gas. Therefore the internal energy of an ideal gas is entirely kinetic energy. For a monoatomic ideal gas this change in internal energy is given by If rotation and vibrational kinetic energies are involved (polyatomic molecules) then f : Number of degrees of freedom of a molecule

Means to Measure Energy Macroscopic Energy: Easy to measure. Microscopic Energy: Needs a detailed experiment. Identify methods to measure economically.

Measurement of Change in Internal Energy First law for A control mass: 1Q2 = U2 – U1 Constant Volume Heating Consider a homogeneous phase of a substance with constant composition. Define Specific Heat: The amount of heat required per unit mass/mole to raise the temperature by one degree. No change in other forms of energy, except internal energy.

Constant Volume Specific Heat The molar specific heat at constant volume is defined by For a monatomic ideal gas,

CV Specific Heats of Ideal Gases Experimental results

Constant Volume Heat Capacity Gas Constant Volume Heat Capacity CV(J/mol K) CV/R Ar 12.5 1.50 He CO 20.7 2.49 H2 20.4 2.45 HCl 21.4 2.57 N2 20.6 NO 20.9 2.51 O2 21.1 2.54 Cl2 24.8 2.98 CO2 28.2 3.40 CS2 40.9 4.92 H2S 25.4 3.06 N2O 28.5 3.42 SO2 31.3 3.76

Polytropic Process of A Closed System Polytropic process of a control mass:

Measurement of Changes during Constant Pressure Process Constant pressure heating of a control mass: Constant Pressure Heating

Changes during Constant Pressure Process Infinitesimal constant pressure heating process by a control mass: The quantity pV is also having a behaviour of property ! This is called flow energy, flow work or internal work. However, the significance of this property is not felt in a Control Mass. Constant Pressure Heating Another way of representing this effect is to combine U and PV. Let this be H.

The issue of Increasing unit Temperature of A Pure Substance

Energy transport by Moving fluid Amount of energy transport by a moving fluid of mass m: Q = mθ = m ( h + ½V2 + gz ) Rate of Energy Transport:

Internal Energy & Enthalpy of Wet Mixtures x is the dryness fraction. U = (1-x) Uf + x Ug Specific Internal energy: Internal energy per unit mass ; u u = (1-x) uf + x ug Specific enthalpy h = (1-x) hf+ x hg T ufg uf u ug