Question:
A Carnot's heat engine works between the temperatures $427^{\circ} C$ and $27^{\circ} C$. What amount of heat should it consume per second to deliver mechanical work at the rate of $1.0\, kW$ ?
A Carnot's heat engine works between the temperatures $427^{\circ} C$ and $27^{\circ} C$. What amount of heat should it consume per second to deliver mechanical work at the rate of $1.0\, kW$ ?
Updated On: Jan 30, 2025
- 0.417 kcal/s
- 4.17 kcal /s
- 41.7 kcal/s
- 0.212 kcal/s
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The efficiency of the heat engine is
$\eta=1-\frac{T_{2}}{T_{1}}=1-\left(\frac{273+27 K}{273+427 K}\right)=\frac{4}{7}$
But $\eta=\frac{W}{\eta}=\frac{1.0 k W}{4/7}=1.75\, kW$
$=0.417\, Kcal/s$
Thus, the engine would require $417\, cal$ of heat per second, to deliver the requisite amount of work.
$\eta=1-\frac{T_{2}}{T_{1}}=1-\left(\frac{273+27 K}{273+427 K}\right)=\frac{4}{7}$
But $\eta=\frac{W}{\eta}=\frac{1.0 k W}{4/7}=1.75\, kW$
$=0.417\, Kcal/s$
Thus, the engine would require $417\, cal$ of heat per second, to deliver the requisite amount of work.
Was this answer helpful?
0
0
Top Questions on 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
- A Carnot engine operating between two reservoirs has efficiency \(\frac{1}{3}\) When the temperature of cold reservoir raised by \(x\), its efficiency decreases to \(\frac{1}{6}\) The value of \(x\), if the temperature of hot reservoir is \(99^{\circ} C\), will be :
- JEE Main - 2023
- Physics
- carnot cycle
View More Questions
Questions Asked in BITSAT exam
In the given circuit, \(E_1 = E_2 = E_3 = 2V\) and \(R_1 = R_2 = 4\Omega\), then the current flowing through the branch AB is:
- BITSAT - 2024
- electrostatic potential and capacitance
A conducting wire is stretched by applying a deforming force, so that its diameter decreases to 40% of the original value. The percentage change in its resistance will be:
- BITSAT - 2024
- thermal properties of matter
- You measure two quantities as \( A = 1.0 \,m \pm 0.2 \,m \), \( B = 2.0 \,m \pm 0.2 \,m \). We should report the correct value for \( \sqrt{AB} \) as:
- BITSAT - 2024
- distance between two points
- The dimensional formula of latent heat is:
- BITSAT - 2024
- laws of motion
- The dimensions of the coefficient of self-inductance are:
- BITSAT - 2024
- Inductance
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.