EME- Elements of Mechanical Engineering | 1st SEM | Answers for 1st assignment
NOTE:
- Answers to questions 11 and 12 are pending. I'll update them very soon.
- For any clarifications, doubts or suggestions please comment below.
- For any clarifications, doubts or suggestions please comment below.
List of Questions in this post:
(1) Define the
following
(i) Energy (ii) Specific heat
(iii) Zeroth
law of thermodynamics (iv)
Temperature (v) Enthalpy
(2) What do you mean by positive and negative work?
(3) Define pressure, Absolute pressure, gauge pressure, and
atmospheric pressure
(4) What is prime mover ? Give brief classification of prime movers?
(5) State all the laws of thermodynamics?
(6) Give comparison between heat and work
(7) What are the sources of energy?
(8) What is LPG and CNG ?
(9) Explain specific heat? Why gas has a two specific heat?
(10) Explain gas laws and prove PV/T = Constant.
(11) Derive equation for work done and heat transfer in case of (i)
isothermal (ii) isobaric (iii) Reversible adiabatic processes
(12) Prove that pvɤ=Constant
for reversible adiabatic process
(13)
Prove relation CP-CV=R.
(14)
Explain calorific value? What is low and high calorific value ?
Answers:
(1) Define the following
(i) Energy (ii) Specific heat
(iii) Zeroth law of thermodynamics (iv) Temperature (v) Enthalpy
Sol:
(i) Energy: Energy is the capacity of a physical system to perform work.
(ii) Specific heat: The amount of heat needed to raise the temperature of one gram of a substance by one degree Celsius, or to raise the temperature of one pound of a substance by one degree Fahrenheit.
(iii) Zeroth law of thermodynamics: The Zeroth Law of Thermodynamics states that if two bodies are each in thermal equilibrium with some third body, then they are also in equilibrium with each other.
(iv) Temperature: a measure of the warmth or coldness of an object or substance with reference to some standard value.
(v) Enthalpy: a quantity associated with a thermodynamic system, expressed as the internal energy of a system plus the product of the pressure and volume of the system, having the property that during an isobaric process, the change in the quantity is equal to the heat transferred during the process.
(2) What do you mean by positive and negative work?
Sol: When there is displacement due to a force in the direction of the force applied, it is said to be positive work done.
Similarly, when there is a displacement due to a force in a direction opposite to direction of the force applied, it is said to be negative work done.
(3) Define pressure, Absolute pressure, gauge pressure, and atmospheric pressure.
Sol: Pressure: Pressure is defined as force per unit area.
Absolute pressure: total pressure at a point in a fluid equaling the sum of the gauge and the atmospheric pressures.
Gauge Pressure: the amount by which the pressure measured in a fluid exceeds that of the atmosphere / absolute pressure minus the atmospheric pressure / The pressure of a system above atmospheric pressure.
Atmospheric pressure: the pressure exerted by the atmosphere at the earth's surface.
(i) Energy (ii) Specific heat
(iii) Zeroth law of thermodynamics (iv) Temperature (v) Enthalpy
Sol:
(i) Energy: Energy is the capacity of a physical system to perform work.
(ii) Specific heat: The amount of heat needed to raise the temperature of one gram of a substance by one degree Celsius, or to raise the temperature of one pound of a substance by one degree Fahrenheit.
(iii) Zeroth law of thermodynamics: The Zeroth Law of Thermodynamics states that if two bodies are each in thermal equilibrium with some third body, then they are also in equilibrium with each other.
(iv) Temperature: a measure of the warmth or coldness of an object or substance with reference to some standard value.
(v) Enthalpy: a quantity associated with a thermodynamic system, expressed as the internal energy of a system plus the product of the pressure and volume of the system, having the property that during an isobaric process, the change in the quantity is equal to the heat transferred during the process.
(2) What do you mean by positive and negative work?
Sol: When there is displacement due to a force in the direction of the force applied, it is said to be positive work done.
Similarly, when there is a displacement due to a force in a direction opposite to direction of the force applied, it is said to be negative work done.
(3) Define pressure, Absolute pressure, gauge pressure, and atmospheric pressure.
Sol: Pressure: Pressure is defined as force per unit area.
Absolute pressure: total pressure at a point in a fluid equaling the sum of the gauge and the atmospheric pressures.
Gauge Pressure: the amount by which the pressure measured in a fluid exceeds that of the atmosphere / absolute pressure minus the atmospheric pressure / The pressure of a system above atmospheric pressure.
Atmospheric pressure: the pressure exerted by the atmosphere at the earth's surface.
4) What is prime mover ? Give brief classification of prime movers?
Sol: Prime mover is device,which use the energy from natural sources and convert it into the mechanical energy.
The prime movers are classified based on the sources of energy utilized by them.The classification is shown below:
1)Thermal prime movers: These are the prime movers which use the thermal energy of source to generate power. Various thermal prime movers are given below:
Fuels (heat engines):
These prime movers use various fuels like petrol, diesel, oil, gas to generate mechanical power.
Heat engines are two types:
-External combustion engines:
1)Reciprocating steam engines
2)Steam turbine
3)Closed cycle gas turbine
-Internal combustion engines:
1)Reciprocating I.C. engines
2)Open cycle gas turbine
Nuclear(nuclear power plant):
This prime mover uses the heat energy of atoms by fission or fusion process to develop the mechanical power. It is mainly used in nuclea power plants. Various radioactive elements like uranium, thorium are used for these fission or fusion process in a nuclear reactor.
Geothermal:
In this type of prime mover the heat energy is obtained from a certain depth or the hot part of the earth below earth surface then it is converted into mechanical by proper engine.
Bio gas:
Bio gas is mainly produced from a garbage or any other waste which is used to produce power by prime mover in a biogas plant.
Solar energy:
The solar energy come to the earth in the form of radiation or electromagnetic waves. This energy trapped in with the help of solar panel made up of semiconductor material. This heat energy is then converted into power.
2)Non-thermal prime movers: These kind of prime movers does not use the heat energy to convert it into the mechanical power. The following are the non thermal prime movers:
Hydraulic turbines:
This type of the prime mover uses the stored potential energy of water to generate power.
Wind power:
With the help of wind turbine the wind energy is converted into the power.
Tidal power:
The energy of tides from ocean is converted into the power by the use of turbnine which is known as tidal power.
(5) State all the laws of thermodynamics?
Sol: The first law, also known as Law of Conservation of Energy, states that energy cannot be created or destroyed in a chemical reaction.
The second law of thermodynamics states that the entropy of any isolated system not in thermal equilibrium almost always increases.
The third law of thermodynamics states that the entropy of a system approaches a constant value as the temperature approaches absolute zero.
(6) Give comparison between heat and work.
Sol: Similarities:
- both heat and work are directional quantities.
- heat and work are only recognized when energy crosses the systems boundaries.
- both heat and work are associated with a process as the system follows a path from one state towards another state
Differences:
- Heat is the random motion of molecules, while work is the ordered motion in one direction.
- It can be proven that work can be totally converted to heat, but heat cannot be 100% converted to work.
- In such a heat to work conversion, the randomness of the universe decreases. This is forbidden by the second law of thermodynamics.
- Heat is a function of state, while work is a function of path.
- Heat is a form of energy, while work is a method of transferring energy.
(7) What are the sources of energy?
Sol: There are 10 main different sources of energy that are used in the world to generate power.
1. Solar Energy
Solar power harvests the energy of the sun through using collector panels to create conditions that can then be turned into a kind of power.
2. Wind Energy
By using large turbines to take available wind as the power to turn, the turbine can then turn a generator to produce electricity.
3. Geothermal Energy
Geothermal energy is the energy that is produced from beneath the earth.
4. Hydrogen Energy
Hydrogen is available with water(H2O) and is a tremendous source of energy and can be used as a source of fuel.
5. Tidal Energy
Tidal energy uses rise and fall of tides to convert kinetic energy of incoming and outgoing tides into electrical energy.
6. Wave Energy
Wave energy is produced from the waves that are produced in the oceans.
7. Hydroelectric Energy
The power of the water is used to turn generators to produce the electricity that is then used.
8. Biomass Energy
Biomass energy is produced from organic material and is commonly used throughout the world.
9. Nuclear Power
The energy is created through a specific nuclear reaction, which is then collected and used to power generators.
10. Fossil Fuels (Coal, Oil and Natural Gas)
Igniton of fossil Fuels provides energy.
(8) What is LPG and CNG ?
Sol: CNG is Compressed Natural Gas, which is mainly methane compressed at a pressure of 200 to 248 bars.
LPG is Liquefied Petroleum Gas, a mixture of propane and butane liquefied at 15 °C and a pressure of 1.7 - 7.5 bar.
(9) Explain specific heat? Why gas has a two specific heat?
Sol: The specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius.
Gas has two specific heat capacities because it has two variables pressure and volume sensitive. These are significant in case of gas. We can assume one of them is fixed when we supply heat. If volume of the gas is constant and heat is supplied. Then we define specific heat is called specific heat at constant volume (Cv). Similarly at constant pressure we define specific heat as Cp.
(10) Explain gas laws and prove PV/T = Constant.
Sol: Boyle's Law: states that for given mass of gas at a constant temperature, the product of the pressure multiplied by the volume is a constant.
Charles's Law/Gay-Lussac's Law: states that for a fixed mass of gas
i) the volume of a gas is directly proportional to the absolute temperature (K) at constant pressure
or
(ii) the pressure of a gas is directly proportional to the absolute temperature (K) at constant volume
If all the laws described above are combined,
p x V = constant (boyle's Law)
V/T = constant (Charles Law)
p/T = constant
We get the following expression,
p x V/T = a constant
(11) Derive equation for work done and heat transfer in case of (i) isothermal (ii) isobaric (iii) Reversible adiabatic processes
Sol: PENDING
(12) Prove that pvɤ=Constant for reversible adiabatic process
Sol: PENDING
(13) Prove relation CP-CV=R.
Sol:
Consider ‘n’ moles of an ideal gas contained in a cylinder fitted with a frictionless piston. If the piston is fixed and the gas is heated, its volume remains constant and all the heat supplied goes to increase the internal energy of the molecules due to which the temperature of the gas increases. If DQv is the amount of heat supplied and DT is the rise in temperature then,
DQv = n CvD T
The pressure of the gas increases during this process, but no work is done because the volume is kept constant.
Hence D W = 0.
applying first law of thermodynamics
Heat supplied = Increase in internal energy + Work done
DQv = D U + 0
DQv = D U
OR
nCvD T = D U
If the piston is free to move, the gas may be allowed to expand at a constant pressure. Let the amount of heat supplied is now is DQp. The addition of heat causes two changes in the system:
-Increase in internal energy
-Work done against external pressure
According to the first law of thermodynamics:
DQ = DU + DW {But DW = PDV}
DQP = DU + PDV
Since DQp = nCpDT
and DU = nCvDT , therefore,
nCpDT = nCvDT + PDV....................(1)
We know that PV = nRT
At T1 Kelvin: PV1 = nRT1 .....(a)
At T2 Kelvin: PV2 = nRT2.....(b)
Subtracting (a) from (b)
PV2 - PV1= nRT2 - nRT1
P(V2 - V1)= nR(T2 - T1) {(V2 - V1) = DV and (T2 - T1) = DT }
PDV = nRDT
Putting the value of PDV in equation (1).
nCpDT = nCvDT + nRDT
nCpDT = nDT(Cv + R)
Cp = (Cv + R)
Cp - Cv = R
(14) Explain calorific value? What is low and high calorific value ?
Sol: Calorific value is the quantity of heat produced by the complete combustion of a given mass of a fuel, usually expressed in joules per kilogram.
Lower calorific value of a fuel portion is defined as the amount of heat evolved when a unit weight (or volume in the case of gaseous fuels) of the fuel is completely burnt and water vapor leaves with the combustion products without being condensed.
Higher calorific value of a fuel portion is defined as the amount of heat evolved when a unit weight (or volume in the case of gaseous fuels) of the fuel is completely burnt and the products of combustion cooled to the normal conditions (with water vapor condensed as a result). The heat contained in the water vapor must be recovered in the condensation process.
Enjoy!
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