Second Law of Thermodynamics - Mechanical Engineering (MCQ) questions and answers

ANSWER: [COP]_H.P. = 1 + [COP]_ref

Explanation:
The COP of a device, operating in a cycle is given by,
[COP] = Desired effect / Work input
In refrigerator,



the desired effect is to maintain temperature of the body A lower than the surrounding temperature.
Therefore, A refrigerator is a device, which operates in a cycle and maintains the temperature a particular body lower than the surrounding temperature.
[COP]_ref = Desired effect / Work input
[COP]_ref = Q2 / W

[COP]_H.P
And in heat pump,



the desired effect is to maintain temperature of the body B more than the surrounding temperature.
Therefore,
[COP]_H.P. = Desired effect / Work input
[COP]_H.P = Q1 / W

and the work input is given by,
W = Q1 – Q2

From the equations of [COP]_ref and [COP]_H.P ,
[COP]_H.P. = 1 + [COP]_ref

ANSWER: perpetual motion machine of second kind (PMM2)

Explanation:
When a heat engine produces net work output by exchanging heat with only one reservoir, then it will be represented as,



In the above diagram, the heat engine is utilizing input heat energy and converting it completely into work output. According to the Kelvin-Planck statement of second law of thermodynamics, it is impossible to produce a heat engine, whose sole effect is to absorb energy in the form of heat from a heat source and produce an equal amount of work. This is due to that some heat has to be rejected to sink. Therefore this heat engine violates the Kelvin-Planck statement of second law of thermodynamics. Hence it will be a perpetual motion machine of second kind (PMM2). PMM2 is impossible to produce.

ANSWER: either a. or b. or both

Explanation:
A reversible process is carried out infinitely slowly, so that every state passed through by the system is an equilibrium state. In the irreversible process every state will not be an equilibrium state as it is carried out very fast. Only the first and the last state of the irreversible process are the equilibrium states. Therefore lack of equilibrium is a cause of irreversibility.
In a dissipative effect the energy is transformed from one form to another form and the final form of energy has a less capacity to do mechanical work. Thus this process becomes irreversible. Therefore involvement of dissipative effect is another cause of irreversibility.

ANSWER: total heat input to the cycle (Q_in) to net work output of the cycle (W_net)

Explanation:
In heat engine cycle, the heat is transferred to the system and work is transferred from the system. The main function of heat engine is to produce work output continuously by consuming heat energy given to the system. So the net work (W_net) and heat supplied (Q_in) to the system are taken into account. The net work output is the difference between work produces in the process and the work input required to take the system to initial state. In stem power plant, net work output is,
Turbine Work (W_T) – Pump Work (W_P)
Therefore, the efficiency of heat engine cycle is the ratio of total heat input to the cycle (Q_in) to net work output of the cycle (W_net).

ANSWER: both a. and b.

Explanation:
PMM2 (Perpetual Motion Machine of the Second Kind) is a hypothetical machine which violates the second law of thermodynamics. Kelvin-Planck as well as Clausius statement both represents the second law of thermodynamics. The Kelvin-Planck statement is related to heat engine whereas the Clausius statement is related to heat pump.

If a machine violates one of the two statements then the other statement is always violated. Therefore, PMM2 is the machine which violates both Kelvin-Planck as well as Clausius statement of second law of thermodynamics.

ANSWER: 75 %

Explanation:
Heat engine is operated between the temperatures

T1 = 927 0C = 927 + 273 = 1200 K and
T2 = 27 0C = 27 + 273 = 300 K

The maximum efficiency of a heat engine is given by,

η_max = 1 – (T2/T1)
η_max = 1 – (300/1200)
η_max = 0.75

ANSWER: (1)-(C), (2)-(D), (3)-(B), (4)-(A)

Explanation:
If the irreversibility is due to a finite pressure gradient, it is called as mechanical irreversibility. Thus, free expansion of gas in a system is the example of mechanical irreversibility.

It the irreversibility is due to a finite temperature gradient, it is called as thermal irreversibility. Thus, melting of ice cube under the sunlight is the example of mechanical irreversibility.

If the irreversibility is due to a finite concentration gradient or chemical reaction in the system, it is called as chemical irreversibility. Thus, forming of water by combination of Hydrogen and Oxygen is the example of mechanical irreversibility.

In refrigeration cycle, irreversibility occurs due to temperature difference between the source and a working fluid that is refrigerant at heat supply and the temperature difference between the sink and the refrigerant at heat rejection.

ANSWER: external irreversibility

Explanation:
All the spontaneous processes are irreversible in nature. The irreversibility is caused by finite potential gradient like temperature gradient etc. or by any dissipative effect like friction. There are two types of irreversibility

i.) Internal irreversibility
ii.) External irreversibility

The external irreversibility occurs due to the temperature difference between the source and a working fluid at heat supply and the temperature difference between the sink and the working fluid at heat rejection. If the hypothetical heat source and sink is considered then the process becomes reversible.

ANSWER: internal irreversibility

Explanation:
All the spontaneous processes are irreversible in nature. The irreversibility is caused by finite potential gradient like temperature gradient etc. or by any dissipative effect like friction. There are two types of irreversibility

i. Internal irreversibility
ii. External irreversibility

Internal irreversibility is caused by internal dissipative effects in the system like friction, turbulence, electric resistance etc. Thus the irreversibility in the system caused by friction is an example of internal irreversibility.

ANSWER: increases

Explanation:
The efficiency of a reversible heat engine is operating between a source at T1 and a sink at T2 is given by,

η = Work done / Heat supplied

η_rev = η_max = ( T1 – T2 ) / T1

η_rev = 1 – (T2/T1)

From the above equation, as T2 decreases the efficiency increases and tends towards 100%