Gas Power Cycles Questions and Answers

Answer: C

The Otto cycle is also known as the constant volume cycle.

The air-standard Otto cycle, the ideal cycle of petrol engines, consists of isentropic compression, heat addition at constant volume, isentropic expansion and heat rejection at constant volume. Heat is added almost instantaneously when the spark ignites the charge with the piston near top dead centre, so the volume hardly changes during combustion.

The constant pressure cycle is the Diesel cycle, and heat is not added at constant temperature in either; that describes the isothermal processes of the Carnot cycle.

Answer: D

It improves both thermal efficiency and specific power output.

Heat exchange (regeneration) uses the hot turbine exhaust to preheat the compressed air before it enters the combustion chamber, so less fuel is needed for the same turbine inlet temperature and the thermal efficiency rises.

Reheating the gas between turbine stages raises the work obtained per kilogram of air, which increases the specific power output. On its own, reheating tends to lower efficiency because the exhaust leaves hotter, but with a heat exchanger that extra exhaust heat is recovered, so the combination improves both. That rules out the options naming only one or neither.

Answer: D

The Diesel cycle is also known as the constant pressure cycle.

In the air-standard Diesel cycle, heat is added at constant pressure: fuel is injected and burns gradually as the piston moves down from top dead centre, so the pressure stays roughly constant while the volume increases. The other processes are isentropic compression, isentropic expansion and heat rejection at constant volume.

The constant volume cycle is the Otto cycle of petrol engines. Neither cycle adds heat at constant temperature, and 'constant heat cycle' is not a standard name.

Answer: B

In the Diesel cycle heat is supplied at constant pressure.

The air standard Diesel cycle has isentropic compression, heat addition at constant pressure while the piston moves, isentropic expansion, and heat rejection at constant volume.

Constant volume heat addition belongs to the Otto cycle. Constant temperature heat addition belongs to the Carnot cycle, and the adiabatic processes are the compression and expansion strokes, where no heat is exchanged.

Answer: D

The efficiency is option D, \(1 - \frac{1}{r_{p}^{(\gamma-1)/\gamma}}\), which the paper prints with y and Y both standing for \(\gamma\).

For the Brayton cycle the temperature ratio across isentropic compression is \(T_{2}/T_{1} = r_{p}^{(\gamma-1)/\gamma}\), and the efficiency is one minus its reciprocal.

\[ \eta = 1 - \frac{1}{r_{p}^{(\gamma - 1)/\gamma}} \]

The form \(1 - 1/r^{\gamma-1}\) is the Otto cycle efficiency, where r is a compression ratio, so A is the trap. B and C use exponents that do not come from the isentropic relation.

Answer: A

The thermal efficiency is 20%.

The net work is the turbine output minus the compressor work, and efficiency is net work over heat supplied.

\[ \begin{aligned} W_{net} &= 600 - 400 = 200\ \text{kJ/kg} \\ \eta &= \frac{200}{1000} = 20\% \end{aligned} \]

60% uses the turbine output alone and 40% the compressor work alone, forgetting that the compressor is driven by the turbine.

Answer: B

The Diesel cycle consists of two reversible adiabatics, one isobar and one isochore.

The air-standard Diesel cycle has four processes: isentropic compression, heat addition at constant pressure (the isobar), isentropic expansion, and heat rejection at constant volume (the isochore).

Two adiabatics and two isobars describe the Brayton (Joule) cycle of the gas turbine. Two adiabatics and two isothermals describe the Carnot cycle. The Otto cycle, not offered, has two adiabatics and two isochores. The combination with one isothermal and one isochore is not a standard air-standard cycle.

Answer: D

The Diesel cycle efficiency is \(1 - \frac{1}{\gamma r^{\gamma - 1}} \frac{(\rho^{\gamma} - 1)}{(\rho - 1)}\).

Heat is added at constant pressure and rejected at constant volume, so

\[ \begin{aligned} \eta &= 1 - \frac{c_{v}(T_{4} - T_{1})}{c_{p}(T_{3} - T_{2})} \\ &= 1 - \frac{1}{\gamma} \cdot \frac{T_{4} - T_{1}}{T_{3} - T_{2}} \end{aligned} \]

Writing every temperature in terms of \(T_{1}\) using the compression ratio r and the cut-off ratio \(\rho\) gives \(T_{2} = T_{1}r^{\gamma - 1}\), \(T_{3} = \rho T_{2}\) and \(T_{4} = T_{1}\rho^{\gamma}\). Substituting yields the expression above.

The bracket \(\frac{\rho^{\gamma} - 1}{\gamma(\rho - 1)}\) is always greater than 1, which is why a Diesel cycle is less efficient than an Otto cycle of the same compression ratio. Option C has this ratio upside down, and options A and B put \(\gamma\) and \(r^{\gamma - 1}\) in the wrong places.

Answer: B

A gas turbine works on the Brayton cycle.

The Brayton (Joule) cycle has four processes: isentropic compression in the compressor, heat addition at constant pressure in the combustion chamber, isentropic expansion in the turbine, and heat rejection at constant pressure. This is exactly the sequence in a gas turbine.

The Otto cycle is the ideal cycle of petrol engines, the Dual cycle that of high-speed diesel engines, both with heat added in a closed cylinder. The Rankine cycle is the cycle of steam power plants, in which the working fluid changes phase.

Answer: C

A gas turbine works on the Bryton (Brayton) cycle.

The Brayton or Joule cycle consists of isentropic compression in the compressor, heat addition at constant pressure in the combustion chamber, isentropic expansion in the turbine, and heat rejection at constant pressure.

The Rankine cycle is for steam power plants, the Otto cycle for petrol engines, and the Stirling cycle for external combustion engines with regenerators.