Question:
A Carnot engine has efficiency of $50 \%$ .If the temperature of sink is reduced by $40^{\circ} C$, its efficiency increases by $30 \%$ .The temperature of the source will be :
A Carnot engine has efficiency of $50 \%$ .If the temperature of sink is reduced by $40^{\circ} C$, its efficiency increases by $30 \%$ .The temperature of the source will be :
Updated On: Feb 12, 2024
- $166.7 \,K$
- $255.1 \,K$
- $266.7\, K$
- $367.7 \,K$
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The correct answer is (C) : \(266.7\, K\)
Efficiency , \(η=1-\frac{T_L}{T_H}\)
Given : η = 50%
\(\therefore\frac{1}{2}=1-\frac{T_L}{T_H}\)
when η increases by 30% then,
\(\frac{1}{2}(1.3)=1-(\frac{T_L-40}{T_H})\)
\(⇒\frac{1}{2}(1.3)=\frac{1}{2}+\frac{40}{T_H}\)
\(\therefore T_H=266.7\ K\)
Was this answer helpful?
0
1
Top Questions on carnot cycle
- A Carnot engine operates between temperatures of $ 600 \, \text{K} $ and $ 300 \, \text{K} $. If it absorbs $ 900 \, \text{J} $ of heat from the source, how much work does it perform?
- BITSAT - 2025
- Physics
- carnot cycle
- A Carnot engine operates between a hot reservoir at 500 K and a cold reservoir at 300 K. Calculate the efficiency of the engine.
- AP PGECET - 2024
- Nano Technology
- carnot cycle
- Identify the equation typically used to describe the efficiency of a cyclic process.
- AP PGECET - 2024
- Nano Technology
- carnot cycle
- The P-V diagram of a Carnot's engine is shown in the graph below. The engine uses 1 mole of an ideal gas as working substance. From the graph, the area enclosed by the P-V diagram is
[ The heat supplied to the gas is 8000 J ]
- KCET - 2023
- Physics
- carnot cycle
- In a Carnot’s engine, as the gas gives heat energy to the sink, then the temperature of the sink
- AP EAPCET - 2023
- Physics
- carnot cycle
View More Questions
Questions Asked in JEE Main exam
- Let \( P_n = \alpha^n + \beta^n \), \( P_{10} = 123 \), \( P_9 = 76 \), \( P_8 = 47 \), and \( P_1 = 1 \). The quadratic equation whose roots are \( \frac{1}{\alpha} \) and \( \frac{1}{\beta} \) is:
- JEE Main - 2025
- Sequences and Series
- The value of \( (\sin 70^\circ)(\cot 10^\circ \cot 70^\circ - 1) \) is:
- JEE Main - 2025
- Trigonometric Identities
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is:
- JEE Main - 2025
- Relations and functions
- Let \( f(x) = \frac{x - 5}{x^2 - 3x + 2} \). If the range of \( f(x) \) is \( (-\infty, \alpha) \cup (\beta, \infty) \), then \( \alpha^2 + \beta^2 \) equals to.
- JEE Main - 2025
- Functions
- A force of 49 N acts tangentially at the highest point of a sphere (solid of mass 20 kg) kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is:
- JEE Main - 2025
- Quantum Mechanics
View More Questions
Concepts Used:
Carnot Cycle
Carnot's Theorem:
From the second law of thermodynamics, two important results are derived where the conclusions are taken together to constitute Carnot’s theorem. It may be stated in the following forms.
- ‘No engine can be more efficient than a perfectly reversible engine working between the same two temperatures’.
- ‘The efficiency of all reversible engines, working between the same two temperatures is the same, whatever the working substances’.
Carnot’s Ideal Heat Engine
- A cylinder having perfectly non-conducting walls, a perfectly conducting base and is provided with a perfectly non-conducting piston which moves without friction in the cylinder. The cylinder contains one mole of perfect gas as the working substance.
- Source: A reservoir maintained at a constant temperature T1 from which the engine can draw heat by perfect conduction. It has an infinite thermal capacity and any amount of heat can be drawn from it at constant temperature T1.
- Heat insulating stand. A perfectly mom-conducting platform acts as a stand for adiabatic processes.
- Sink: A reservoir maintained at a constant lower temperature T2 (T2 < T1) to which the heat engine can reject any amount of heat. The thermal capacity of sink is infinite so that its temperature remains constant at T2, no matter how much heat is given to it.