Question:medium
As shown in the figure, five Carnot engines, each with efficiency \(\eta\) and same number of cycles per unit time, are operating between six heat reservoirs. The amount of heat released per cycle by one engine is completely absorbed by the next engine. Consider \(Q_0\) to be the amount of heat absorbed per cycle by the first engine and \(W\) as the amount of total work done by all the engines per cycle, then the net efficiency of the system is found to be
\[
\eta_{\mathrm{net}}
=
\frac{W}{Q_0}
=
\frac{211}{243}
\]
The value of \(\eta\) is _______.
As shown in the figure, five Carnot engines, each with efficiency \(\eta\) and same number of cycles per unit time, are operating between six heat reservoirs. The amount of heat released per cycle by one engine is completely absorbed by the next engine. Consider \(Q_0\) to be the amount of heat absorbed per cycle by the first engine and \(W\) as the amount of total work done by all the engines per cycle, then the net efficiency of the system is found to be
\[
\eta_{\mathrm{net}}
=
\frac{W}{Q_0}
=
\frac{211}{243}
\]
The value of \(\eta\) is _______.
Show Hint
For cascaded engines:
\[
Q_n=Q_0(1-\eta)^n
\]
and:
\[
\eta_{\mathrm{net}}
=
1-(1-\eta)^n
\]
for \(n\) identical stages.
Updated On: May 20, 2026
Show Solution
Solution and Explanation
Was this answer helpful?
0
Top Questions on Thermodynamics
- The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have:
- JEE Main - 2025
- Physics
- Thermodynamics
- Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.
Reason (R): In an isothermal process, \( PV = \text{constant} \), while in an adiabatic process \( PV^\gamma = \text{constant} \). Here, \( \gamma \) is the ratio of specific heats, \( P \) is the pressure and \( V \) is the volume of the ideal gas.
In the light of the above statements, choose the correct answer from the options given below:- JEE Main - 2025
- Physics
- Thermodynamics
- A poly-atomic molecule (C\(_3\)R, \(C_v = 4R\), where \(R\) is gas constant) goes from phase space point A (\(P_A = 10^4 \, \text{Pa}, V_A = 4 \times 10^{-3} \, \text{m}^3\)) to point B (\(P_B = 5 \times 10^4 \, \text{Pa}, V_B = 6 \times 10^{-7} \, \text{m}^3\)) to point C (\(P_C = 10^4 \, \text{Pa}, V_C = 8 \times 10^{-3} \, \text{m}^3\)). A to B is an adiabatic path and B to C is an isothermal path. The net heat absorbed per unit mole by the system is:
- JEE Main - 2025
- Physics
- Thermodynamics
- If \[ \text{C(diamond)} \rightarrow \text{C(graphite)} + X \, \text{kj mol}^{-1} \] \[ \text{C(diamond)} + \text{O}_2(g) \rightarrow \text{CO}(g) + Y \, \text{kj mol}^{-1} \] \[ \text{C(graphite)} + \text{O}_2(g) \rightarrow \text{CO}(g) + Z \, \text{kj mol}^{-1} \] At constant temperature. Then:
- JEE Main - 2025
- Chemistry
- Thermodynamics
- Want to practice more? Try solving extra ecology questions todayView All Questions
Questions Asked in JEE Advanced exam
A thin uniform rod of length L and certain mass is kept on a frictionless horizontal table with a massless string of length L fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point O. If a horizontal impulse P is imparted to the rod at a distance x = L/n from the mid-point of the rod (see figure), then the rod and string revolve together around the point O, with the rod remaining aligned with the string. In such a case, the value of n is _____.
- JEE Advanced - 2024
- Friction