A thermodynamic cycle is composed of four processes. The heat added, and the work done in each process are as follows:
The thermal efficiency of the cycle is
Thermal efficiency is defined as
Where Q2 is the heat rejected from the system and Qt is the heat added to the system.
Here Q2 = 50 J
Q1 = 80 J
A heat reservoir is maintained at 927 °C. If the ambient temperature is 27 °C, the availability of heat from the reservoir is limited to
Availability is the maximum useful work that can be extracted from the system working between two reservoirs.
Availability of Heat =
Which of the following devices complies with the Clausius statement of the second law of thermodynamics?
Clausius statement: No device can operate on a cycle and produce effect that is solely the heat transfer from a lower-temperature body to a higher-temperature body.
Clausius statement is related to refrigerator and heat pump whereas gas turbines works on Brayton Cycle.
Two reversible engines are connected in series between a heat source and a sink. The efficiencies of these engines are 60% and 50%, respectively. If these two engines are replaced by a single reversible engine, the efficiency of this engine will be
Let we supply 1 kJ of hat to engine 1 and the rejected heat of engine 1 will go to engine 2.
Now, if both engines are replaced by a single engine. So,
∴ Efficiency of new engine = 1−0.21 = 0.8 = 80%
Short trick: -
ηoverall = η1 + η2 - η1η2
= 0.6 + 0.5 - 0.6 × 0.5 = 0.8 = 80%
The entropy of water at 0 K is assumed to be
Absolute zero (0 K) is a state at which the enthalpy and entropy of a system reach their minimum value, taken as 0.
In mathematical term,
S = k ln W
Where, S is entropy
k is Boltzmann constant
W is thermodynamic probability
When W = 1, it represents the greatest order, S = 0. This occurs only at T = 0 K.
This statement is also known as Third law of thermodynamics.
The property of a working system which changes as the heat is supplied to the working fluid in a reversible manner is known as ________.
Entropy is a property which is a measure of energy dispersion in a system or the irreversibility. Entropy transfer is associated with heat transfer. If the heat is added to the system, then its entropy increases and if heat is lost from the system, its entropy decreases.
Two reversible heat engines operating between temperatures 2000 K and T K and T K and 500 K respectively. What is the intermediate temperature, if the efficiency of both the cycles is same?
Efficiency of first engine (E1),
Efficiency of second engine
As efficiency of both engine is same,
So, η1 = η2
⇒ T2 = 2000 × 50
When efficiency of both engines are equal, then intermediate temperature
A Carnot heat engine is working with an efficiency of 50%. If the cycle is converted into a heat pump after reversing, then what is the coefficient of performance of the heat pump?
Efficiency of Carnot engine (ηE) = 50%
If a Carnot heat engine which is operating between two temperature limits is converted to heat pump then
An inventor says, he has invented an engine which will reject 20% of heat absorbed from the source and the engine operates between 2000 K and 500 K. What kind of engine it is?
T1 = 2000 K
T2 = 500 K
Since, the actual efficiency is more than the Carnot efficiency, so this engine has an impossible cycle.
In a cyclic process, the work done by the system is 20 kJ, -30 kJ, -5 kJ and 10 kJ. What is the net heat (kJ) for the cyclic process?
dQ = dW + ΔU (As per first law)
For the cyclic process,
ΔU = 0
∴ W = 20 - 30 - 5 + 10
= -5 kJ
The heat rejection takes place in Carnot cycle at _______.
A Carnot cycle consists of the four processes:
The triple point on a T-s diagram is ________.
The pressure and temperature at which three phases of a pure substance coexist is called triple point. The triple point is merely the point of intersection of the sublimation and vaporization curves. It has been found that on a ‘p-T’ diagram the triple point is represented by a point and on a ‘p-v’ and T-s diagram it is a line, and on a ‘u-v’ diagram it is a triangle. In the case of ordinary water, the triple point is at a pressure of 4.58 mm Hg and a temperature of 0.01OC.
Which gas can attain the highest efficiency for the same compression rise?
γmonoatomic> γdiatomic> γtriatomic
As efficiency is directly proportional to the ratio of specific heat (γ), so monoatomic will have the highest efficiency.
A tank containing air is stirred by a paddle wheel. The work input to the paddle wheel is 9000 kJ and heat transferred to the surroundings from the tank is 3000 kJ. The external work done by the system is:
First law of thermodynamics:
(-3000) = ΔU + (-9000)
ΔU = 6000 kJ
As there is 9000 kJ work done on the system, no work will be done by the system. Energy will be stored in the system as internal energy.
If pressure at any point in the liquid approaches the vapor pressure, liquid starts vaporising and creates pockets or bubbles of dissolved gases and vapours. This phenomenon is ________.
At the boiling point, the saturated vapor pressure is equal to atmospheric pressure. Due to this pressure equalisation bubbles formation take place so the vaporization becomes a volume phenomenon.
Cavitation is the phenomenon of the formation of vapour bubbles of a flowing liquid in a region where the pressure of the liquid falls below the vapour pressure and sudden collapsing of these vapour bubbles in a region of higher pressure. When the vapour bubbles collapse, a very high pressure is created. The metallic surfaces, above which the liquid is flowing, is subjected to these high pressure which cause pitting action on the surface. Thus cavities are formed on the metallic surface and hence the name is cavitation.
Two gases A and B with their molecular weights 28 and 44 respectively, expand at constant pressures through the same temperature range. The ratio of quantity of work done by the two gases (A : B) is ________.
Work done, W = P2V2 - P1V1
A series of operations, which takes place in a certain order and restore the initial conditions at the end, is known as
A process is reversible if, after it has been carried out, it is possible to restore both the system and its entire surroundings to exactly the same states they were in before the process.
If the system and its surroundings cannot return to their initial states at the end of the reversed process, this process is an irreversible process.
A thermodynamic cycle consists of a linked sequence of thermodynamic processes that involve transfer of heat and work into and out of the system, while varying pressure, temperature, and other state variables within the system, and that eventually returns the system to its initial state. Two primary classes of thermodynamic cycles are power/engine cycles and heat pump cycles. Power cycles are cycles which convert some heat input into a mechanical work output, while heat pump cycles transfer heat from low to high temperatures using mechanical work input.
Specific heat of a gas, Cp = Cv, at
The specific heat of solids and liquids and the specific heats (both at constant volume and constant pressure) of ideal gases are essentially functions of temperature only. At T = 0K i.e, at the absolute zero thermodynamic temperature one should have the values of specific heats as zero putting T = 0K in the expressions for specific heats.
This strictly means at an absolute temperature of 0K we would need no energy at all to raise the temperature of unit mass of a substance by unit degree rise in temperature. But as soon as the temperature rises by even an infinitesimal amount, we have some value of the specific heat and it increases with temperature and hence more and more energy would be needed to achieve a similar rise in temperature as temperature increases.
Joule-Thompson coefficient for an ideal gas is
Joule Thomson Coefficient:-
For an ideal gas, μ = 0, because ideal gases neither warm not cool upon being expanded at constant enthalpy.
A thermometer works on the principle of
A thermometer works on the principle of Zeroth law of Thermodynamics.
According to Zeroth Law of thermodynamics, if two bodies are in thermal equilibrium with a third body then the two bodies are also in thermal equilibrium with each other.
Thermometer are based on the principle of finding the temperature by measuring the thermometric property.
The measurement of temperature is performed by the thermometer by using mercury, which - when heated - expands, and contracts in response to a fall in temperature. This causes the length of the liquid column to be longer or shorter depending on the temperature.