Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason $R$
Assertion A: Efficiency of a reversible heat engine will be highest at $-273^{\circ} C$ temperature of cold reservoir
Reason R: The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as $n =\left(1-\frac{T_2}{T_1}\right)$
In the light of the above statements, choose the correct answer from the options given below
Assertion A: Efficiency of a reversible heat engine will be highest at $-273^{\circ} C$ temperature of cold reservoir
Reason R: The efficiency of Carnot's engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as $n =\left(1-\frac{T_2}{T_1}\right)$
In the light of the above statements, choose the correct answer from the options given below
- $A$ is true but $R$ is false
- Both $A$ and $R$ are true and $R$ is the correct explanation of $A$
- Both $A$ and $R$ are true but $R$ is NOT the correct explanation of $A$
- A is false but $R$ is true
The Correct Option is B
Solution and Explanation
Assertion A is true, stating that the efficiency of a reversible heat engine will be highest at -273°C (0 Kelvin), which is the temperature of the cold reservoir.
Reason R is also true, explaining the efficiency of Carnot's engine using the formula: η = 1 - \(\frac {T_2}{T_1}\), where Tc is the temperature of the cold reservoir and Th is the temperature of the hot reservoir.
However, Reason R doesn't directly explain why the efficiency is highest at -273°C, which is stated in Assertion A. The formula in Reason R does show how the efficiency is affected by the temperatures of both the hot and cold reservoirs, but it doesn't directly correlate with the statement in Assertion A about the temperature of -273°C being the point of highest efficiency.
So, the correct option is (B) : Both A and R are true and R is the correct explanation of A
Top Questions on Thermodynamics
Match List-I with List-II.
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Concepts Used:
Thermodynamics
Thermodynamics in physics is a branch that deals with heat, work and temperature, and their relation to energy, radiation and physical properties of matter.
Important Terms
System
A thermodynamic system is a specific portion of matter with a definite boundary on which our attention is focused. The system boundary may be real or imaginary, fixed or deformable.
There are three types of systems:
- Isolated System – An isolated system cannot exchange both energy and mass with its surroundings. The universe is considered an isolated system.
- Closed System – Across the boundary of the closed system, the transfer of energy takes place but the transfer of mass doesn’t take place. Refrigerators and compression of gas in the piston-cylinder assembly are examples of closed systems.
- Open System – In an open system, the mass and energy both may be transferred between the system and surroundings. A steam turbine is an example of an open system.
Thermodynamic Process
A system undergoes a thermodynamic process when there is some energetic change within the system that is associated with changes in pressure, volume and internal energy.
There are four types of thermodynamic process that have their unique properties, and they are:
- Adiabatic Process – A process in which no heat transfer takes place.
- Isochoric Process – A thermodynamic process taking place at constant volume is known as the isochoric process.
- Isobaric Process – A process in which no change in pressure occurs.
- Isothermal Process – A process in which no change in temperature occurs.
Laws of Thermodynamics
Zeroth Law of Thermodynamics
The Zeroth law of thermodynamics states that if two bodies are individually in equilibrium with a separate third body, then the first two bodies are also in thermal equilibrium with each other.
First Law of Thermodynamics
The First law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic processes, distinguishing three kinds of transfer of energy, as heat, as thermodynamic work, and as energy associated with matter transfer, and relating them to a function of a body's state, called internal energy.
Second Law of Thermodynamics
The Second law of thermodynamics is a physical law of thermodynamics about heat and loss in its conversion.
Third Law of Thermodynamics
Third law of thermodynamics states, regarding the properties of closed systems in thermodynamic equilibrium: The entropy of a system approaches a constant value when its temperature approaches absolute zero.