11th Class Physics Chapter 11 Heat and Thermondyanmics Short Questions Answer

There is a large number of molecules in a gas. According to our assumption, equal number of molecule move in all direction. It means that the number of molecules moving to the right in x – direction is equal to the number of molecules moving to the left in the opposite direction with the same velocity. Thus, the voter sum of their velocities will be zero. But the square of the negative velocity i.e. [(-v²) = v²]is also a positive, therefore the average of the square of the velocities will not be zero.

When a car is driven through some distance, work done by the car is partly spent in overcoming the frictional force between the road and the car tyre. Some part of work done against friction is converted into heat which rises the temperature of the gas in a car tyre. As we know that pressure is directly proportional to absolute temperature at constant volme, therefore the pressure must increase because the heat energy increases the velocity and collisions of gas molecules. As a result, molecular collisions against the walls of a tyre increase the pressure of air inside the tyre.

In all these cases, sine the system (gas) to returns to its initial state after undergoing a cyclic process, so internal energy of the system does not change.

When a glass is heated at constant pressure, then the heat supplied is used in two ways
(i) Some part of heat is used doing the external work to move the piston up against the constant atmospheric pressure.
(ii) The other part of heat is used to increase the internal energy and temperature.
If the same gas is heated at constant volume, no external work is done to expend the gas. The total heat supplied is used to increase the the internal energy and temperature of the gas. This shows that more heat is required to heat the gas at constant pressure than at constant volume for the same rise of temperature. So we conclude that specific heat at constant pressure is greater than the specific heat at constant volume i.e. C_P > C_v

Adiabatic process is an example of such a procers. Consider a gas enclosed in a non- conducting cylinder by a non – conducting piston. If the gas is compressed, the work done on the gas will increase its temperature but no heat will leave the system. Conversely if the gas is allowed to expend, the woke done by the gas at the cost of its internal energy will increase its expansion of the gas is adiabatic in nature because no heat is transferred to or more from the system but its temperature changes.

Yes, it is possible to convert internal energy into mechanical energy Applying the first law of thermodynamics to an adiabatic process. Q = ΔU +W In such process, Q = 0 then ΔU = W If work done ‘W’ is negative, than the work is done at the cost of internal energy. This means if a system (gas) is allowed to expend adiabatically some work is done at the cost of internal energy. Thus, internal energy decreases because some quantity of internal energy has been converted into mechanical work. Yes, it is possible to convert internal energy into mechanical energy Applying the first law of thermodynamics to an adiabatic process. Q = ΔU +W In such process, Q = 0 then Δ U = W If work done ‘W’ is negative, than the work is done at the cost of internal energy. This means if a system (gas) is allowed to expend adiabatically some work is done at the cost of internal energy. Thus, internal energy decreases because some quantity of internal energy has been converted into mechanical work. Examples :- (1) Gases can be liquefied by this process. (2) In case be heart engines (e.g. petrol engine), the hot gases exapand and the piston moves backward. In this way also, internal energy is converted into work (i.e. mechanical energy)

No, it is not possible to construct a heat engine that will not expel heat into the atmosphere. According to second law of thermodynamics, all the practical heat engine absorb heat from the source, convert a part of it into the mechanical work and reject the remainder to the cold body or atmosphere. Hence, no heat engine can operate with a single source for conversion of the heat into the mechanical work without expelling heat to the atmosphere. In other words, there must be a temperature difference between the hot and cold bodies (source and sink) for the conversion of heat into mechanical work.

When the milk is shaken rapidly, the kinetic energy of the molecules of the milk increases which causes an increase in the temperature and internal energy. No heat is added to the milk. While we are shaking the milk, we do some work on it, which is converted into K.E. of molecules of milk.

An running air conditioner, placed on a table in the middle room, reject the heat through the compressor in the same room. Thus, no change in the room temperature will take place because the heat absorbed from the room is expelled or lost in the same room. Hence, there will be no effect on the temperature of the room.

Yes, the mechanical energy of work can be completely converted into heat energy. When work (mechanical energy) is done is compressing the gas by adiabatic process, the increase in the internal energy ‘ΔU’ of the gas is equal to the work done W on it. According to lst law of thermodynamics, Q = Δ U – W But Q = 0, and W = negative (work done on gas) 0 = Δ U – W or Δ U= W Reason:- The whole of the mechanical energy can be absorbed by the molecules of the gas in the form of their K.E. this K.E gets converted into heat. EXAMPLES:- (1) When breaks of speeding car are applied, it stop which means that all of its K.E. Is converted into heat. Second law of thermodynamics does not apply when work is being converted into heat. (2) If we rub our hands, by rubbing them the whole mechanical energy is converted into heat energy

If the work is done by friction, the work will be converted ito heat. The heat produced due to friction goes into the surrounding i.e. air and becomes useless. No useful work can be performed by it due to the unavailability of this energy, we can say that the entropy will increase when work is done by friction. Hence, the entropy of a system increases due to friction.

When ice melts due to high temperature of its surrounding ‘s’, it is converted into water. The heat ΔQ transferred to ice from surroundings at absolute temperature T is positive. Thus, entropy of melted ice (i.e water) increases by the following equation ΔS =Δ Q/T As ΔS is positive, therefore, the entropy of this natural process (i.e melted ice) increases.

Examples :- (i) The rapid escape of air from a burst tyre. (ii)The rapid expansion and compression of air through which a sound wave is passing. (iii) Cloud formation in the atmosphere under adiabatic process.

Temperature is the average kinetic of molecules of a substance while heat is the sum of kinetic energy of all the molecules of a substance. The Si unit of temperature is Kelvin (K) while the heat of joule because heat is a form of energy.

Cannot engine has been proposed by sadi Carnot as an ideal heat engine which is free from friction and heat losses. Therefore, its efficiency is maximum. But all real heat engine are less efficient than Carnot engine due to friction and other heat losses. According to Carnot’s Theorm, not heat engine can be more efficient than a Carnot engine operating between the same two temperature.

Solution:-
From kinetic theory of gases, we have the relation
P = 1/3/ N₀ <mv²>
Where     N₀ = No of molecules in a unit volume
m = mass of one molecule
N₀m = mass of unit volume of the gas. But mass per unite volume is called density of gas
or          N₀m = P
Hence P = 1.3 (N₀) <mv²> = 1/3 N₀m<v²>
Or        P = 1/3 p <v²>
Hence P = <v²> = 3P/p

The percentage efficiency of a Carnot engine is given by percentage efficiency = (1 – T2/T1)*100 This equation shows that the efficiency of a Carnot engine will be one or 100% if t2 =oK. This means Q2 = o and the work done by Carnot engine is equal to Q1 (W= Q1- Q2 = Q1)I.e. all the heat absorbed by the engine is converted into work which is impossible. This violates the second law of thermodynamics. Hence it is not possible to achieve the temperature of absolute zero. Although the efficiency of Carnot engine is maximum but it is always less than one or 100%.

In the petrol engine, the petrol is converted into vapours and then mixed with air form an explosive mixture. In this engine, a spark plug is needed to burn the mixture. The operation of petrol engine is difficult and its efficiency is smaller (30%) than that of diesel engine (40%) In diesel engines, air is compressed to a pressure of about 35 atmospheres. It becomes so hot that a jet of crude oil can burn in it. Thus we have to use no spark plug in the diesel engine. The cruid oil used in this engine has less fire risk and is cheaper than petrol. These useful feature have made the diesel engine popular and is being used in cars, buses and ships.

When the automobile is driven on the motorway, force of friction is produced between tyre and the road. In order to overcome the friction, the work done by the engine is converted into heat in the tyre. The gas inside the tyre becomes hot. The heat increases the molecular velocities of the gas. The increase in velocity increases the number of collisions against the walls of the tyre. Thus the pressure of the gas in tyre increases. The tyre due to the increase of pressure may burst. Therefore, we should reduce the pressure of the gas in the typre for the protection of our lives, While moving on motorway.

Pressure of a gas According to the kinetic theory of gases, a gas consists of a very large number of molecules which are continuously moving at random in all directions with velocities from zero to a very high value. These molecule suffer elastic collisions with the walls of the container and exert forces. The total force exerted by the molecules per unit area of the walls gives the pressure of the gas enclosed in a vessel. Thus according to kinetic theory, the pressure of the gas is due ti the striking of the molecules with the walls of the container.

Solution-
                     Temperature in centigrade = T_c = 37 ⁰C
Temperature in Fahrenheit= T_f = ?
Temperature in Kelvin        = T_k = ?
Using the formula to convert Centigrade into Fahrenheit
T_f = 9/5 T_c+ 32
Putting the value, we get
T_f = 9/5*37+32= 333/5+32
or T_f = 66.6.+32=98.6 ⁰ F
T_f = 98.6 ⁰F
(ii) Formula to convert centigrade into Fahrenheit
T_k = 37+273=310k
T_k     = 310 k                ans.

Real gases, such as hydrogen and etc, do not obey the gas laws exactly because (i) their molecules have definite size, and (ii) they attract each other mutally. Real gases, however obey the gas laws at low pressures and high temperature. If the pressure is raised higher and higher, keeping the temperature constant, the volume according to Boyle’s law must go on decreasing and approach zero fore every high pressure. If case of a real gas, the volume can never zero at any pressure as its molecules occupy space. Moreover, when a real gas is compressed, the distance between the molecules decreases and they attract each other. This attraction helps to compress the gas and makes its volume a bit smaller than it would be if there were no attraction between the molecules.

It is defined as the measure of the disorder of a system. Conside a reversible process during which a system absorbs a quantity of heat ΔQ at absolute temperature ‘T’. The increase in entropy ΔS is given by ΔS = ΔQ/T change in entropy ‘ΔS’ is taken as positive if heat is adden to the system. It is as negative if heat is proved or rejected from the system.

Entropy of a system will decrease if heat is removed from the system without any change in its temperature. Example:- Consider an example of heat engine. Entropy of the source (HTR) of a heat engine heat engine decreases when heat flows from the source into the cylinder at its temperature. On the other hand, entropy of the sink of the heat engine increases due to transfer of heat into it.

Molar specific heat of a temperature is defined as the amount of heat required to raise the temperature of one mole of the substance through l K. It is denoted by C Mathematically, it is expressed as C = Q/ ΔT Where ‘Q’ is the amount of heat supplied to the substance to raise the temperature ‘ΔT’

It is customary to define molar specific heat of a gas in two following wats.
(i) Molar specific heat at constant volume.
(ii) Molar specific heat at constant pressure.
(i)       Molar specific heat at constant volume (C_v)
It is defined as the amount of heat required to raise the temperature of on mole of a gas through l K at constant volume, It is denoted by ‘C_v)
Mathematically it is expressed as Δ
C_v = Q_v/ ΔT
Where ‘Q_v’ is the amount of heat supplied at constant volume and It is customary to define molar specific heat of a gas in two following wats.
(i) Molar specific heat at constant volume.
(ii) Molar specific heat at constant pressure.
(i)       Molar specific heat at constant volume (C_v)
It is defined as the amount of heat required to raise the temperature of on mole of a gas through l K at constant volume, It is denoted by ‘C_v)
Mathematically it is expressed as Δ
C_v = Q_v/ ΔT
Where ‘Q_v’ is the amount of heat supplied at constant volume and T is rise of temperature.
(ii) Molar specific heat at constant pressure (C_p)
It is defined as the amount of heat required to raise the temperature of one mole of a gas through l K at constant pressure. It is denoted by C_p.
Mathematically, it is written as
Q_p = C_p Δ_T  =     or      C_p = Q_p/ ΔT
Where Q_p is the amount of heat supplied at constant pressure. It is customary to define molar specific heat of a gas in two following wats.
(i) Molar specific heat at constant volume.
(ii) Molar specific heat at constant pressure.
(i)       Molar specific heat at constant volume (C_v)
It is defined as the amount of heat required to raise the temperature of on mole of a gas through l K at constant volume, It is denoted by ‘C_v)
Mathematically it is expressed as Δ
C_v = Q_v/ ΔT
Where ‘Q_v’ is the amount of heat supplied at constant volume and ΔT is rise of temperature.
(ii) Molar specific heat at constant pressure (C_p)
It is defined as the amount of heat required to raise the temperature of one mole of a gas through l K at constant pressure. It is denoted by C_p.
Mathematically, it is written as
Q_p = C_p Δ_T  =     or      C_p = Q_p/ ΔT
Where Q_p is the amount of heat supplied at constant pressure.ΔT is rise of temperature.
(ii) Molar specific heat at constant pressure (C_p)
It is defined as the amount of heat required to raise the temperature of one mole of a gas through l K at constant pressure. It is denoted by C_p.
Mathematically, it is written as
Q_p = C_p Δ_T  =     or      C_p = Q_p/ ΔT
Where Q_p is the amount of heat supplied at constant pressure.

The branch of physics which deals with the transformation of heat energy into mechanical energy is called thermodynamics. There are a few terms which are often used in thermodynamics such as system, heat engine, Thermal equilibrium. And states.

In any thermodynamics process, When heat ‘Q’ is added to a system, this energy appears as an increase in the internal energy ‘Δu’ stored in the system plus the work ‘w’ done by the system on its surroundings. This is called first law of thermodynamics. Mathematically, it can be written as Q = ΔU + W (i) ‘Q’ is positive when heat enters the system and negative when it leaves the system. (ii) ‘W’ is positive when work is done by the system and negative when work is done on the system. (iii) ΔU is positive when temperature of the system rises and negative when temperature of system falls.

Sadi cannot in 1840 proposed an ideal heat engine which is free from friction and heat losses. He described it using only isothermal and adiabatic processes. He showed that its efficiency would be maximum when heat engine works in an reversible cycle between two heat reservoirs at different temperature. But its effectively cannot be 100%. The effectively of an actual engine is less than that of Carnot engine.

It states that “no heat engine can be more efficient than a Carnot engine (reverse engine) working between the same two temperatures. Practically, the cold reservoir is nearly at room temperature. Therefore, the efficiency can only be increased by raising the temperature of hot reservoir. All real heat engines are less efficient than Carnot engine due to friction and other heat losses.

The concept that matter is made up molecules which are in continuous random motion is called the kinetic theory. The kinetic theory of gases explains the behavior of gases in terms of interaction of molecules and energy they have. This is supposed by the phenomenon of diffusion of gases and Brownian motion of smokes particles. The kinetic theory uses the idea that movement of gas molecules is responsible for pressure of gas.

1) A finite volume of gas consist of very large number of molecules. (2) The size of the molecules is much smaller than the separation between molecules (3) The gas molecules are in random motion moving with different velocities and changing their direction after very collision. (4) Molecules do not exert force on each other except during a collision. (5) The gas molecules make elastic collisions with another and with the walls of the container in which the gas is kept.

Isothermal process:- It is that process in which the temperature of the system remain constant. Example:- In deriving Newton’s formula for the speed of sound in air, he assumed that during compression and rarefaction, the rise and fall of temperature balance each other and so the temperature of the medium remains constant. Thus he concluded that sound travels through air under isothermal conditions (i.e. no change in temperature) Adiabatic Process A process in which no heat enters or leaves the system is called an adiabatic process. Examples:- (i) The rapid expansion and compression of air through which a sound wave is passing, cause the change in temperature of the gas. So change in pressure and volume obey adiabatic gas law Pvy = constant (ii) Could formation in the atmosphere under adiabatic process.

The process which can be retraced in exactly reverse direction without producing any change in the surrounding is called reversible process. Example:- When an elastic spring is compressed slowly, some work is done upon it . Now if the applied force is gradually decreased, the spring expands and does nearly the same amount of work itself as was done initially upon it. Hence, the process of gradual compression and extension of a spring is nearly reversible.

Triple point of water is a state where ice, water and vapours all have the common temperature and pressure. The value of triple point of water is 273.16 K.

Boyle’s law states that for the given mass of the gas the volume is inversely proportional to the pressure at constant temperature of the gas.

A four stroke petrol also undergoes four successive process in each cycle such as in Carnot cycle. The working substance is air which is heated by the combustion of some fuel (petrol) in the cylinder of the engine itself. The expansion of hot air converts some heat into work. The principle of its working lines on four processes in each cycle.

As we know that the pressure of the gas is expressed as
P  = 1/3 N₀m <v²>……………..(1)
we have
N₀m = Number of molecules in unit volume of gas *mass of the gas molecules.
= Mass of unit volume of the gas
= Density of the gas
(Because density= mass/volume)
Therefore, the equation (1) become
P = 1/3 p<v²>

Charles’s law states that for a given mass of the gas, the volume is directly proportional to the absolute temperature of the gas if the pressure is kept constant. Mathematically, it is expressed as V α T Or V/T = constant

We know the formula for the pressure of the gas on the kinetic theory of gas, which is given as
P= 2/3 N₀ <1/2 mv²>
But          N₀ = N/V = No. of molecules / Volume
P = 2/3 N/V<1/2mv²>
Or            PV= 2/3N<1/2 mv²>…………………………….(1)
If average translational K.E. <1/2mv²> remains constant, the temperature of the gas will remain constant and 2/3 N is also constant.
So equation (1) becomes
PV = constant
Which is the required equation of Boyle’s law.

The formula of pressure is given by
P = 2/3 N₀<1/2mv²>
But N₀ = N/V = No. of molecules/volume
P          = 2/3 N/V<1/2mc²>
or    V = 2/3 N/P<1/2mv²>
Since <1/2mv²>αT
V/T = 2/3 N/P…………………………………(1)
If pressure ‘P’ is kept constant, the light hand side of equ. (1) becomes constant
Hence, V/T = constant
This is required equation of Charle’s law.

As we know that pressure of the gas is P = 2/3N0<1/2mv2> But No = N/V = No of molecules per unit volume P = 2/3N/V<1/2mv2> Or PV = 2/3N<1/2mv2> But PV = NKT NKT = 2/3N<1/2mv2> or T =2/3k <1/2mv2> or T = cosnt. <1/2mv2> Hence, Tα

The sum of all forms of molecular energies (such as kinetic and optional energies) of a substance is called internal energy. Example:- What two objects are rubbed together their internal energy increases due to conversion of mechanical energy into heat. This is the reasons that rubbing of two ice pieces causes melting of ice. Any increase in temperature indicates the increase in the eternal energy.

A system is a collection of matter which has a distinct boundary. For example, the gas in the balloon acts as a system, the boundary of which is the balloon itself. Another example is a gas enclosed in cylinder fitted with a piston.

Def- A device which converts heat energy into mechanical energy (i.e.work) is called heat engine. Principle:- Heat engine takes heat energy from a hot body converts a part of heat into work and rejects the remaining part of heat to cold body. It means that two bodies at diffract temperature are necessary for the operation of a heat engine.

When the temperature of source and sink of a heat engine become equal, than the change in entropy is maximum.

A process which cannot be retraced in the backward (opposite) direction by reversing the controlling factors, is called an irreversibleprocess. Example:- (i) If some current is passing through a conductor, some heat is produced if the direction of electric current is reversed heat is gain produced. Hence, floe of the electric current through a conductor is an irreversible process. (ii) An explosion provides an example of highly irreversible process. (iii) Work done against friction is also its eample.

The molar gas constant per mole of the gas is called Boltzmann constant. It is denoted by ‘K/
It  is expressed by the formula
Boltzmann constant = R = R/N₀
Knowledge the values,
Molar gas constant = R = 8.314 jmol^-1k^-1
Number of molecules in a mole  = Avogadro’s N₀= 6.02*10³³
K = 8.31/6.02*10²³ = 1.38*10^-23Jk^–

It is impossible to cause heat to flow from a cold body to a hot body without the expenditure of energy.

It is possible to construct a heat engine working continuously in a cycle, takes heat from a hot reservoir (source) and converts it completely into work.

The efficiency ‘ɳ’ of the Carnot heat engine is defined by
ɳ = out put /input = Net work done/Heat energy absorbed
= ΔW/Q₁ = Q₁-Q₂/Q₁
or ɳ = 1- Q₂/Q₁
Since    T₂/T₁= Q₂/Q₁
ɳ = 1- T₂/ T₁
Where T₁ and T₂ are the temperature of source and sink respectively.