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The correct ANSWER is (c) True only for calorically perfect gas

Explanation: The TOTAL ENTHALPY of a steady, inviscid, adiabatic gaseous flow is constant. For a calorically perfect gas the total enthalpy can be written in terms of total temperature TIMES the specific heat at constant pressure (which is also a constant). THUS, the total temperature is also a constant.

Right option is (C) h0 is not equal to the FREESTREAM value

Best explanation: h0 is the stagnation enthalpy for the steady, inviscid, adiabatic flow which is equal to the static enthalpy plus kinetic ENERGY, all PER unit mass. If all the streamlines originate from a common freestream, stagnation enthalpy is equal to the freestream value and is CONSTANT along the flow i.e. same for all streamlines.

Right CHOICE is (a) TRUE always

The best I can EXPLAIN: The isothermal and isentropic compressibility for a fluid are PRECISE thermodynamic properties of the fluid. The values have already been found and compiled in various handbooks for EASY reference.

The correct choice is (d) H1=H2 for adiabatic FLOW

Easy EXPLANATION: The TOTAL enthalpy at two points along the flow may or may not be equal in general. The total enthalpies are equal in case of an adiabatic flow between the two points in CONSIDERATION.

The CORRECT choice is (a) False

Easy EXPLANATION: Isentropic process seems restrictive in a practical case, i.e. a process which is both reversible and adiabatic is not feasible. This is what we think generally. Actually, a LARGE number of practical compressible flow cases are good ASSUMPTIONS of isentropic PROCESSES only.

Right ANSWER is (c) Isentropic process

Explanation: A reversible process is one in which no DISSIPATIVE phenomena occur. An adiabatic process is one in which no HEAT EXCHANGE is there between the system and the SURROUNDINGS. A process that is both adiabatic and reversible is called an isentropic process.

Correct OPTION is (c) T*

The BEST I can explain: The T* is defined as the temperature at a point where the local STATIC temperature is T, in the sonic flow when the fluid element is speeded up to sonic VELOCITY adiabatically. ALSO, T* is the temperature when the supersonic fluid element is slowed down to sonic velocity adiabatically.

The correct option is (a) High PRESSURE change

The BEST I can explain: The pressure change can be both high or low and we can’t ascertain it with the GIVEN information. MOREOVER, for LIQUIDS the compressibility is negligible and so we can assume that density change is also small. Hence, the flow is compressible.

The correct answer is (C) Volume increases

To EXPLAIN: When a gas is COMPRESSED, the temperature and pressure increases. This is observed in real life also. The volume of the gas decreases DUE to compression. Heat is transferred in or out of the SYSTEM also.

The correct answer is (C) T ds = DE + p dv

The explanation: The first law of thermodynamics when expressed in terms of entropy gives us two alternate equations. These equations are T ds = de + p dv and T ds = dh – V dp. We have USED the relation of heat and entropy in the first law EQUATION to get these equations.

The correct option is (d) Displacement of system boundary: DQ

To explain I would SAY: The CHANGE in dq or dw brings a change in de. Displacement of system boundary or squeezing of system volume are sources of dw. While heating and absorbing of RADIATION by mass in the system are sources of dq, therefore de.

The correct choice is (d) Zero always

To explain: The enthalpy is a state function. This is true for all type of gases. It is conserved for a REVERSIBLE process (SINCE no generation of ENTROPY takes place due to DISSIPATION). From the formula, it is visible that entropy always is a function of two thermodynamic VARIABLES (p, T) or (v, T), etc. It is not zero always.

Right choice is (a) v1 = v2

To explain: In isentropic flow, between any two points, the stagnation quantities are same. They are constant ALONG the entire isentropic flow. THUS, ρo,1 = ρo,2; po,1 = po,2 and ho,1 = ho,2 while the VELOCITIES are not EQUAL necessarily. So, V1 is not equal to V2.

Correct answer is (a) \(\frac {p_2}{p_1} =(\frac {T_2}{T_1} )^{\frac {\gamma }{\gamma -1}}\)

To elaborate: The isentropic relation means no heat exchange and no DISSIPATIVE forces. Also, for the calorically perfect gas, specific heats are CONSTANT. When we put these conditions in the entropy EQUATION, we obtain the relation between pressure and TEMPERATURE which is \(\frac {p_2}{p_1} =(\frac {T_2}{T_1} )^{\frac {\gamma }{\gamma -1}}\).

Correct answer is (a) Density increases

For explanation: The formula for compressibility when expressed in terms of density GIVES a DIRECT RELATION between pressure change and density change. i.e. dρ = ρ τ DP. HENCE, when the pressure increases density of the fluid increases.

Correct answer is (d) Static Pressure

Easy explanation: Gases are the most randomly moving MOLECULES. The pressure due to this RANDOM motion of gas molecules is the static pressure. It is as if we are RIDING along with the gas at the LOCAL flow VELOCITY.

Right choice is (d) Mass DIFFUSION occurs

For explanation: Reversible process has no dissipative effects i.e. viscosity and mass diffusion are absent. Also, WORK in a reversible process is given as DW = -pdv. Therefore, the first equation of THERMODYNAMICS can be written as dq – pdv = DE.

Correct choice is (a) False

Explanation: The STAGNATION quantities (TOTAL pressure, total temperature, total density ETC) are defined quantities and exist in the flow at each point as if we are actually stopping the FLUID particle. In reality, we don’t have to bring the fluid particles to REST to calculate them.

The correct option is (b) False

Best explanation: At any point ALONG the flow where static density and PRESSURE are defined, we can assign the VALUES of STAGNATION density and pressure. The definition of these involves the isentropic compression to zero velocity but the flow need not be isentropic. These CONCEPTS are valid for all general flows, including non isentropic flow at any point.

The correct choice is (a) CP-cv=2R

Easiest explanation: The SPECIFIC heat ratio of a gas is defined as the ratio \(\frac {c_p}{c_v}\) and the difference in cp and cv is defined as the universal gas constant. From these, the FOLLOWING RELATIONS for the specific heat of an ideal gas are obtained cp=\(\frac {\gamma R}{\gamma -1}\) and cv=\(\frac {R}{\gamma -1}\).

Correct choice is (d) Liquid FLOW

The explanation is: For an inviscid, adiabatic and steady flow we can show that H + V^2/2 = constant. This is valid along any streamline. It does not take into ACCOUNT the flow being a liquid flow and is valid for gaseous flows ALSO.

Correct answer is (b) True

Explanation: The boundary layer regime over flow has dissipative EFFECTS and VISCOSITY. This is not isentropic. But the flow outside has negligible viscosity, dissipative effects. Thus, it is a reversible process to a good APPROXIMATION. Moreover, there is no heat exchange taking PLACE to or from the fluid element, making this an ADIABATIC flow. So, outside the boundary layer, the flow is isentropic.

The correct choice is (d) Ice will melt

Explanation: The second law of THERMODYNAMICS states which direction the process will TAKE place, unlike the first law which just tells whether the process is possible or not. From entropy considerations, ice will melt in this case. This is VISIBLE from real life OBSERVATION as well. Total entropy has to increase or stay the same.

Correct answer is (a) ds=0

Easy explanation: The change in entropy is zero only for an adiabatic PROCESS of a GAS. Calorically perfect gas has constant specific heats, which makes the integration between the INITIAL and final state easier. The final FORM of the equation comes out as s2-s1=cvln\(\FRAC {T_2}{T_1}\)+Rln\(\frac {v_2}{v_1}\) and s2-s1=cpln\(\frac {T_2}{T_1}\)-ln\(\frac {p_2}{p_1}\). As visible from these equations s=s(p, T).

Right choice is (c) cp and cp are functions of T

To explain I would SAY: The calorically perfect gases have constant SPECIFIC heats at low temperatures (T < 1000 K). cp and cp are nothing else but specific heat constants at constant pressure and temperature respectively. Internal ENERGY and enthalpy can be given in terms of the specific heats i.e. e=cv T and h=cpT.

Correct choice is (a) True

To explain: By DEFINITION, stagnation enthalpy is the enthalpy of the fluid when the VELOCITY is zero. THUS, putting V = 0 in the equation gives the stagnation enthalpy as the constant because the equation holds for any POINT along the streamline.

Right ANSWER is (b) Mach number

For explanation I WOULD say: Compressibility values gives a good estimate of the nature of fluid i.e. whether it is COMPRESSIBLE or not. But it has exceptions LIKE low SPEED flow over airfoil etc. The Mach number is the best parameter to judge the compressibility of the fluid.

The CORRECT option is (a) True

The explanation is: If we employ some HEAT transfer mechanism such that the TEMPERATURE of the gas is kept CONSTANT during compression, it is called isothermal COMPRESSIBILITY. It is symbolized by τT where T stands for isothermal compression.

Right OPTION is (b) False

The explanation is: The isothermal compression of a gas MEANS that no heat is transferred from the fluid ELEMENT and there is no friction involved. Thus, isothermal compressibility has additional condition of no fiction along with THERMAL compressibility.

Right OPTION is (b) Total change in entropy in a reversible PROCESS is always zero

Explanation: In an irreversible process, entropy is generated. This means the change in entropy for an irreversible process is positive. ALSO, for a reversible process, change in entropy is zero SINCE the entropy is conserved in the universe. Thus, the change in total entropy for an irreversible process is GREATER or equal to zero while that for the reversible process is zero.

The correct OPTION is (c) Pressure

The BEST I can explain: The compressibility is DEFINED as the fractional change in the volume of the fluid element PET unit change in pressure. It is a negative quality since the volume decreases as pressure increases and vice VERSA.

The CORRECT answer is (C) True only for high speeds

Explanation: Gases have high compressibility VALUES which states that for a given PRESSURE change, the density change can be higher giving a compressible flow. But LOW speed flows are an exception since the pressure change across the field is small. This dominates the high compressibility value giving an incompressible flow.

Right answer is (a) de is an exact DIFFERENTIAL

Explanation: The first law in thermodynamics is an empirical relation and has been verified by experiments. It has NEVER been VIOLATED. Exact differential depends only on final and initial points. de is an exact differential while dq and dw are not exact differentials.

The correct option is (d) 8977 J

The explanation: The SPECIFIC enthalpy (h) is GIVEN as h=cpT where T is in Kelvin. This is the enthalpy per unit mass. For TOTAL enthalpy of the air, we need to MULTIPLY h by the molecular mass of air i.e. H=29h which gives total enthalpy equal to 8977 J, irrespective of the PROCESS.