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(a) Boundary

For path 1:

Heat given Q₁ = + 1000 J

Work done = W₁(let)

For path 2:

Work done (W₂) = (W₁ − 100) J

Heat given Q₂ = ?

As change in internal energy between two states for different paths is same.

∴ ∆U = Q₁ − W₁ = Q₂ − W₂

1000 – W₁ = Q₂ − (W₁ − 100)

or  Q₂ = (1000 – 100) J

= 900 J

Mass remains same in this case. Radius of the sphere will increase. Surface area of sphere ∝ (radius)² and Volume ∝ (Raidus)³ so the volume will undergo maximum percentage increase

It is defined as the ratio of the amount of heat removed in a cycle from the refrigerator to the work done by some external agency to help the removal of this heat, i.e.,

β = \(\frac{Q_2}{W}\) = \(\frac{Q_2}{Q_1-Q_2}\)

Also  β = \(\frac{T_2}{T_1-T_2}\)

For higher efficiency of refrigerator, β should be higher.

If brakes were not applied, the car would have come down with acceleration. Hence, application of brakes is preventing this acceleration, i.e., brakes are putting frictional forces on the wheels. The work being done by these frictional forces shows up as heat.

Adiabatic process can bring a change in the internal energy of gas. The gas is compressed, that is work is done on it, its internal energy increases, when the gas is expanded, work id done by the gas, it’s internal energy decreases.

A gas is a vapour above its critical temperature, while vapour is a gas below its critical temperature. Further, a gas cannot be liquefied by applying pressure alone; whereas a vapour can be liquefied by applying pressure only.

Efficiency η = 1 –\(\frac{T_2}{T_1}\)

Where T₂ is the temperature of the sink and T₁ is the temperature of the source.

Also   η = 1 –\(\frac{Q_2}{Q_1}\)

Where Q₂ is the amount of heat rejected to sink and Q₂ is the amount of heat rejected to sink and Q₁ is the amount of heat supplied by the source.

For using the internal energy of sea water to operate the engine of a ship, the internal energy of the sea water has to be converted into mechanical energy. Since whole of the interned energy cannot be converted into mechanical energy, a part has to be rejected to a colder body (sink). Since, no such body is available, so the interned energy of the sea water cannot be used to operate the engine of the ship.

Kelvin’s statement : No process is possible whose sole result is the absorption of heat from a reservoir and complete conversion of the heat into work.

Clausius statement : It is not possible to transfer heat from a body at lower temperature to another at higher temperature without the help of some external energy.

The attraction between molecules is the source of internal P.E. It results in change of distance between the molecules. Increase in internal P.E. increases the distance between the molecules.

Normally the specific heat of a gas varies from zero to infinity are shown here. We have ∆Q = mC∆T, hence specific heat, C = \(\frac{∆Q}{m∆T}\)

(i) When a gas is compressed, its temperature rises without any heat supplied. This mean ∆Q = 0, ∆T ≠ 0 hence, C = 0.

(ii) When a gas is expanded and heated simultaneously, its temperature rise can be zero. Hence ∆Q ≠ 0, ∆T = 0. Hence, C = ∞.

The random motion of molecules is the source of internal K.E. It affects temperature of the substance. Increase in internal K.E. increases temperature of the substance.

If a container has n molecules each of mass m, the pressure inside is P = \(\frac{1}{3}\frac{M}{V}C^2,\) where V is the volume of the container and c is the root mean square speed of the molecules. It is also written as

P = \(\frac{1}{3}\frac{M}{V}c^2\) 

= \(\frac{1}{2}ρc^2\)

In monoatomic gases molecules have only translational K.E., while in diatomic and triatomic gases, molecules have translational, rotational as well as vibrational kinetic energies. Due to presence of other type of motions, more heat is required to produce the transitional K.E. of the molecules and hence their temperature increases by certain amount. The specific heat increases accordingly.

Equal masses of gases have equal amount of internal K.E. at same temperature. In rarefied gas, molecules are at more distance from each other than in compressed gas. These molecules possess more interned P.E. It makes total internal energy of the rarefied gas more than that of the compressed gas.