Heat and Thermodynamics | Physics
Short answer questions:
1. ‘An object contains more heat’- is it a right statement? If not why?
● Heat is not quantity. Heat is energy in transit which flows from higher temperature object to lower temperature object.
● Once the heating process is stopped we cannot use the word heat. Heat is the energy in transit but not energy stored in the body. An object has more heat is wrong, instead object is hot will be appropriate.
2. Obtain an ideal gas law from Boyle’s and Charles’ law.
● According to Boyle's law P α 1 /v
● According to Charle's law V α T. By combining these two equations we have PV = CT. Here C is positive constant.
● Constant C is k times the number of particles N.
Here k is the Boltzmann constant (1.381 × 10-23 JK−1) and it is found to be universal constant. So the ideal gas law can be stated as follows PV = NkT.
3. Define one mole.
One mole of any substance is the amount of that substance which contains Avogadro number (NA) of particles (such as stoms or molecules).
4. Define specific heat capacity and give its unit.
Specific heat capacity of a substance is defined as the amount of heat energy required to raise the temperature of 1kg of substance by 1 Kelvin or 1°C
∆Q = ms ∆T
Therefore s = ( 1/m ) ( ∆Q/∆T )
Where s - specific heat capacity of a substance and its value depends only on the nature of the substance not on the amount of the substance.
∆Q - Amount of heat energy : ∆T - Change in temperature ; m - Mass of the substance ; The SI unit for specific heat capaity is Jkg−1K−1.
5. Define molar specific heat capacity.
● Molar specific heat capacity is defined as heat energy required to increase the temperature of one mole of substance by
1 K or 1°C = 1/μ (∆Q/∆T)
● Here C is known as molar specific heat capacity of a substance and μ is number of moles in the substance.
● The SI unit for molar specific heat capacity is J mol−1 K−1
6. What is a thermal expansion?
● Termal expansion is the tendency of matter to change in shape, area and volume due to a change in temperature.
● All three states of matter (solid, liqid and gas) expand when heated. When a solid is heated, its atoms vibrate with higher amplitude about their fixed points. The relative change in the size of solids is small.
7. Give the expressions for linear, area and volume thermal expansions.
αL= ∆L / Lo∆T; Where αL = coefficient of linear expansion.
∆L = Change in length; Lo = Original length ; ∆T = Change in temperature.
αA = ∆L / Ao∆T ;
Where αA = coefficient of area expansion.
∆A = Change in area ;
Ao = Original area ;
∆T = Change in temperature
αV = ∆A / Vo∆T
Where, αV = coefficient of volume expansion;
∆V = Change in volume ;
Vo = Original volume;
∆T = Change in temperature.
Unit of coefficient of linear, area and volumetric expansion of solids is C−1 or K−1.
8. Define latent heat capacity. Give its unit.
● Latent heat capacity of a substance is defined as the amount of heat energy required to change the state of a unit mass of the material.
Q = m × L ;
L = Q / m
● Where L = latent heat capacity of the substance ; Q = Amount of heat; m = mass of the substance. The SI unit for Latent heat capacity is J kg−1.
9. State Stefan-Boltzmann law.
● Stefan Boltzmann law states that, the total amount of heat radiated per second per unit area of a black body is directly proportional to the fourth power of its absolute temperature.
● E ∝ T4 or E = σT4 ; Where, σ is known as Stefan's constant. Its value is 5.67 × 10-8 W m-2 k-4.
10. What is Wien’s law?
● When's law states that, the wavelength of maximum intensity of emission of a black body radiation is inversely proportional to the absolute temperature of the black body.
● λm ∝ 1/T or λm = b/T.
Where, b is known as Wien's constant.
● Its value is 2.898 × 10-3m k.
11. Define thermal conductivity. Give its unit.
● The quantity of heat transferred through a unit length of a material in a direction normal to unit surface area due to a unit temperature difference under steady state conditions is known as thermal conductivity of a material.
● Q / L = KA∆T / L ; where, K is hnown as the coefficient of thermal conductivity.
● The SI unit of thermal conductivity is Js−1m−1K−1 or Wm−1K−1.
12. What is a black body?
A black body is an object that absorbs all electromagnetic radiations, it is a perfect absorber and radiator of energy with no reflecting power.
13. What is a thermodynamic system? Give examples.
Thermodynamic system: A thermodynamic system is a finite part of the universe. It is a collection of large number of particles (atoms and molecules) specified by certain parameters called pressure (P), Volume (V) and Temperature (T). The remaining part of the universe is called surrounding, Both are separated by a boundary.
Examples: A thermodynamic system can be liquid, solid, gas and radiation. Bucket of water, Air molecules in the room, Human body, Fish in the sea.
14. What are the different types of thermodynamic systems?
Open system: It can exchange both matter and energy with the environment.
Closed system: It can exchange energy, but not matter with the environment.
Isolated system: It can exchange neither energy nor matter with he environment.
15. What is meant by ‘thermal equilibrium’?
Two systems are said to be in thermal equilibrium with each other if they are at the same temperature, which will not change with time.
16. What is mean by state variable? Give example.
In thermodynamics, the state of a thermodynamic system is represented by a set of variables called thermodynamic variables.
Examples: Pressure, temperature, volume and internal energy etc.
The values of these variables completely describe the equilibrium state of a thermodynamic system.
17. What are intensive and extensive variables? Give examples.
Intensive variable depends on the size or mass of the system.
Example: Volume, total mass, entropy, internal energy, heat capacity etc.
Intensive variables do not depend on the size or mass of the system.
Example: Temperature, pressure, specific heat capacity, density etc.
18. What is an equation of state? Give an example.
● The equation which connects the state variables in a specific manner is called equation of state.
● A thermodynamic equilibrium is completely specified by these state variables by the equation of state. If the system is not in thermodynamic equilibrium then these equations cannot specify the state of the system.
● Example of equation of state called vander Walls equation. Real gases obey this equation at thermodynamic equilibrium.
● The air molecules in the room truly obey vander Walls equation of state. But at room temperature with low density we can approximate it into an ideal gas.
19. State Zeroth law of thermodynamics.
The zeroth law of thermodynamics states that if two systems. A and B are in thermal equilibrium with a third system, C, then A and B are in thermal equilibrium with each other.
20. Define the internal energy of the system.
● The internal energy of a thermodynamic system is the sum of kinetic and potential energies of all the molecules of the systern with respect to the center of mass of the system.
● The energy due to molecular motion including translational, rotational and vibrational motion is called internal kinetic energy (EK). The energy due to molecular infraction is called internal potential energy (EP).
Example: Bond energy. U = EK + EP.
21. Are internal energy and heat energy the same? Explain.
● No, but they are related. If heat energy is added to substance, its internal energy will increase. Internal energy is the amount of kinetic and potential energy possessed by particles in a substation.
● Heat energy concerns only transfer of internal energy from the hotter to a colder body.
22. Define one calorie.
The amount of heat required at a pressure of standard atmosphere to rise the temperature of 1g of water 1°C.
23. Did joule converted mechanical energy to heat energy? Explain.
● Yes, In his experiment, two masses were attached with a rope and a paddle wheel. When these masses fall through a distance h due to gravity both the masses lose potential energy equal to 2mgh.
When these masses fall, the paddle wheel turns.
● Due to the turning of wheel inside water, frictional force comes in between the water and the paddle wheel.
● This causes a rise in temperature of the water. This implies that gravitational potential energy is converted to internal energy of water.
● The temperature of water increases due to the work done by the masses.
24. State the first law of thermodynamics.
Change in internal energy (∆U) or the system is equal to heat supplied to the system (Q) minus the work done by the system (W) on the surroundings.
25. Can we measure the temperature of the object by touching it?
● No. When we stand bare feet with one foot on the carpet and the other on the tiled floor.
● Our foot on tiled floor feels cooler than the foot on the carpet even though both the tiled floor and carpet are at the same room temperature.
● It is because the tiled floor transfer the heat energy to our skin at higher rate than the carpet.
● So the skin is not measuring the actual temperature of the object instead it measures the rate of heat energy transfer. But if we place a thermometer on the tiled floor or carpet it will show the same temperature.
26. Give the sign convention for Q and W.
System gains heat - Q is positive
System loses heat - Q is negative
Work done on the system - W is negative
Work done by the system - W is positive
27. Define the quasi-static process.
● A quasi-static process is an infinitely slow process in which the system changes its variables (P.V.T)
● So slowly such that it remains in thermal, mechanical and chemical euilibrium with its surroundings throughout.
By this infinite slow variation, the system is always almost close to equilibrium state.
28. Give the expression for work done by the gas.
In general the work done by the gas by increasing the volume from Vi to Vf is given bty W = vfʃvi pdV
29. What is PV diagram?
PV diagram is a graph between pressure P and volume V of the system. The P-V diagram is used to calculate the amount of work done by the gas during expansion or on the gas during compression.
30. Explain why the specific heat capacity at constant pressure is greater than the specific heat capacity at constant volume.
● Because when heat is added at constant pressure the substance, expands and works, i.e. more amount of energy has to be supplied to a constant pressure to increase the system's temperature by the same amount.
● Some of this energy is lost due to expansion.
31. Give the equation of state for an isothermal process.
The equation of state for isothermal process is given by PV = Constant.
32. Give an expression for work done in an isothermal process.
W = μR T In (vf / vi)
33. Express the change in internal energy in terms of molar specific heat capacity.
If Q is the heat supplied to mole of a gas at constant volume and if the temperature changes by an amount ∆T, we have Q = μCV ∆T …….. (1)
By applying the first law of thermodynamics for this constant volume process (W = O, since dV = O), we have Q = ∆U – O …….. (2)
By comparing the equations (1) and (2),
∆U = μ CV ∆T or CV = 1/μ (dU/dT)
If the limit ∆T goes to zero, we can write
CV = = 1/μ × dU/dT
Since the temperature and internal energy are state variable, the above relation holds true for any process.
34. Apply first law for (a) an isothermal (b) adiabatic (c) isobaric processes.
Isothermal: Q = W; Q - Heat; W - Work
Adiabatic: ∆U = W Isobaric; ∆U = Q - P∆U
∆U - change in internal energy.
35. Give the equation of state for an adiabatic process.
The equation of state for an adiabatic process is given by PVγ = Constant. Here γ is called adiabatic exponent (γ = Cp / Cv )
which depends on the nature of the gas. The equation implies that if the gas goes from an equilibrium state (PiVi) to another equilibrium state (Pf, Vf) adiabatically then it satisfies the relation.
36. Give an equation state for an isochoric process.
The equation of state for an isochoric process is given by P = (μR/v)T,
Where, μR / v = Constant
37. If the piston of a container is pushed fast inward. Will the ideal gas equation be valid in the intermediate stage? If not, why?
Decrease in volume leading to increase in temperature, work is done on the gas. Ideal gas equation PV = RT. When piston be pushed further the parameters V and R are taken as constant. The equation becomes P = kT. i.e. P ∝ T.
38. Draw the PV diagram for
a. Isothermal process
b. Adiabatic process
c. isobaric process
d. Isochoric process
39. What is a cyclic process?
This is a thermodynamic process in which the thermodynamic system returns to its initial state after undergoing a series of changes. Since the system comes back to the initial state, the change in the internal energy is zero. In cyclic process, heat can flow in to system and heat flow out of the system.
40. What is meant by a reversible and irreversible processes?
● A thermodynamic process can be considered reversible only if it possible to retrace the path in the opposite direction in such a way that the system and surroundings pass through the same states as in the initial, direct process.
Example: A quasi-static isothermal expansion of gas, slow compression and expansion of a spring.
Irreversible process: All natural process are irreversible.
● Irreversible process cannot be plotted in a PV diagram, because these processes cannot have unique values of pressure, temperature at every stage of the process.
41. State Clausius form of the second law of thermodynamics
"Heat always flows from hotter object to colder object spontaneously". This is known as the Clausius form of second law of thermodynamics.
42. State Kelvin-Planck statement of second law of thermodynamics.
Kelvin-Planck statement: It is impossible to construct a heat engine that operates in a cycle, whose sole effect is to convert the heat completely into work. This implies that no heat engine in the universe can have 100% efficiency.
43. Define heat engine.
Heat engine is a device which takes heat as input and converts this heat in to work by undergoing a cyclic process.
44. What are processes involves in a Carnot engine?
There are four servisible process in involed in carnot's engine. There are
Step A to B: Quasi-static isothermal expansion .
Step B to C: Quasi-static adiabatic expansion.
Step C to D: Quasi-static Isothermal compression
Step D to A: Quasi-static compression adiabatic compression.
45. Can the given heat energy be completely converted to work in a cyclic process? If not, when can the heat can completely converted to work?
● No. In a cyclic process, the complete heat energy is not completely converted to work.
● The whole heat cannot be converted into work, as it will violate second law of thermodynamics.
● In an Isothermal process the whole heat can be converted into work. For an isothermal process dQ = dT, which shows that whole heat can be converted into work.
46. State the second law of thermodynamics in terms of entropy.
● "For all the processes that occur in nature (irreversible process), the entropy always increases. For reversible process entropy will not change".
● Entropy determines the direction in which natural process should occur.
47. Why does heat flow from a hot object to a cold object?
Because entropy increases when heat flows from hot object to cold object.
48. Define the coefficient of performance.
COP is a measure of the efficiency of a refrigerator, it is defined as the ration of heat extracted from the cold body (sink) to the external work done by the compressor
W. COP = β [ QL / W]