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# Rocket Propulsion – Summary of Thermodynamic Relations

1 - Question

Which of the following comprises of internal thermal energy and flow work?

a) Entropy

b) Enthalpy

c) Kinetic energy

d) Potential energy

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Answer: bExplanation: Enthalpy comprises of flow work and internal thermal energy. Flow work arises when a fluid crosses a boundary with some velocity v. Entropy is a measure of the degree of randomness of a system.

2 - Question

In which of the following cases can enthalpy be expressed as a function of constant Cp and absolute temperature T?

a) Ideal gas

b) Calorically perfect gas

c) Real gas

d) Thermally perfect gas

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Answer: bExplanation: A calorically perfect gas obeys ideal gas law and has constant Cp. A thermally perfect gas obeys ideal gas law, but it has a temperature dependent Cp value. A real gas is an imperfect gas that doesn’t follow the ideal gas relations and has Cp values that are temperature and pressure dependent.

3 - Question

Find the stagnation enthalpy of a calorically perfect gas having a flow velocity of 94 m/s and static temperature of 315 K. (Cp=1005 J/kg/K)

a) 321 kJ/kg

b) 234 kJ/kg

c) 456 kJ/kg

d) 543 kJ/kg

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Answer: aExplanation: Since the gas is calorically perfect, h = Cp T, where h is the static enthalpy and T is the static temperature. h = Cp T = 1005 x 315 = 316,575 J/kg Then using the relation h0 = h + v2/2, h0 = 316,575 + 4324.5 ≅ 321 kJ/kg.

4 - Question

For an incompressible subsonic flow over a nozzle, at a typical location A along the nozzle, the diameter of the cross-section was found to be 30 cm. What will be the diameter of the cross section at a point B where the flow velocity was determined to be twice the value at A?

a) 21.21 cm

b) 42.42 cm

c) 15 cm

d) 60 cm

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Answer: aExplanation: Given flow over the nozzle is subsonic and incompressible. So density doesn’t vary along the nozzle and the flow velocity is less than about 0.3 times the speed of sound. In this case, the product of the nozzle area and flow velocity at any location along the nozzle length remains to be the same. A1V1 = A2 V2 Given V2 = 2 V1 d22/4 = (d12/4) V1/V2 ⇒ d2 = d1 √0.5 = 21.21 cm.

5 - Question

For an isentropic flow along a nozzle, at location A, the static temperature and pressure were measured to be 320 K and 5 bar. What will be the static pressure at the location where the static temperature is 500 K? (Given η = 1.4)

a) 23.8 bar

b) 32.4 bar

c) 12.4 bar

d) 7.4 bar

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Answer: aExplanation: For the isentropic flow, adiabatic relations can be applied (isentropic means reversible as well as adiabatic). Then using P1/P2 = (T1/T2)(η/η-1) P2 = 5 x (500/320)1.4/0.4 ≅23.8 bar.

6 - Question

An isentropic flow at section x has a velocity of 200 m/s and static enthalpy of 360 kJ/kg. Determine the flow velocity at a location y where the static enthalpy is half the value at x.

a) 447.2 m/s

b) 385.9 m/s

c) 515.4 m/s

d) 408.2 m/s

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Answer: aExplanation: For an isentropic flow, stagnation enthalpy remains constant. Stagnation enthalpy h0 = h + v2/2 is constant. So h1 + v12/2 = h2 + v22/2 v2 = √2(360,000 – 180000 + 40000/2) = 447.2 m/s.

7 - Question

Which of the following is not a unit of gas constant?

a) J/(mol.K)

b) kcal/(K.mol)

c) m3atm/(K.mol)

d) amu.m2s2/K

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Answer: dExplanation: The unit amu corresponds to the unified mass unit or atomic mass unit. The correct expression should have been amu.m2/(s2.K).

8 - Question

For an isentropic flow of air through a pipe from a large chamber having a pressure of 5 MPa and temperature of 290 K, determine the temperature at a point along the length of the pipe where the pressure is 3 MPa.

a) 250 K

b) 277 K

c) 219 K

d) 300 K

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Answer: aExplanation: In the large chamber, the flow can be assumed to be stagnant. Given that the flow is isentropic, adiabatic relations can be applied to the flow. Using P/P0 = (T/T0)(η/η-1) and taking the value of to be 1.4 (for air), T = (3/5)0.4/1.4 x 290 ≅250 K.

9 - Question

Which of the following doesn’t happen during a subsonic and isentropic nozzle expansion?

a) Increase in the specific volume

b) Decrease in absolute fluid static temperature

c) Decrease in static pressure

d) Decrease in stagnation temperature

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Answer: dExplanation: Stagnation temperature for an isentropic process remains constant. Static temperature, static pressure, and specific volume may vary.

10 - Question

Acoustic velocity in ideal gases is independent of _____________

a) nature of the gas

b) gas temperature

c) gas pressure

d) the molecular mass of the gas

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Answer: cExplanation: Acoustic velocity (a) is the same as the velocity of sound in the medium under consideration. It is dependent on the nature of the medium, its temperature, and its molar mass. This can be observed from the relation a = (ηRT)−−−−−√, where η is the ratio of specific heats (which depends upon the type of gas), R is the gas constant for the particular gas (R = Ru/M, where Ru is universal gas constant and M is the molar mass of the gas) and the gas temperature (T).