Thermodynamics System and Processes MCQ Quiz - Objective Question with Answer for Thermodynamics System and Processes - Download Free PDF

Explanation:

Zeroth Law of Thermodynamics

• The Zeroth Law of Thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. This law provides a fundamental basis for the concept of temperature.

Working Principle: The Zeroth Law essentially implies that temperature is a fundamental and measurable property of matter. If system A is in thermal equilibrium with system C, and system B is also in thermal equilibrium with system C, then system A and system B must be in thermal equilibrium with each other. This logical reasoning allows for the establishment of temperature as a transitive property.

Significance in Measurement of Temperature: The Zeroth Law is crucial because it allows for the creation of temperature scales and the use of thermometers. It enables us to compare temperatures of different systems and ensures that thermometers can provide consistent and reliable temperature readings.

Applications: The principles of the Zeroth Law are applied in various fields, including:

• Thermometry: The development and calibration of thermometers rely on the Zeroth Law, ensuring accurate temperature measurement.
• Engineering: Temperature control and monitoring in processes such as heating, cooling, and chemical reactions are based on the Zeroth Law.
• Scientific Research: Accurate temperature measurement is essential in experiments and studies involving thermal properties of materials and systems.

Explanation:

Conservation of Energy in Mechanical Systems

• The conservation of energy principle states that energy can neither be created nor destroyed; it can only be transformed from one form to another. In the context of mechanical systems, this principle reduces to conserving mechanical energy when the system operates under certain idealized conditions. Mechanical energy includes kinetic energy and potential energy, both of which are associated with the motion and position of objects, respectively.
• In fluid systems, this principle is applied with considerations for the compressibility and thermodynamic properties of the fluid. The specific case where the conservation of energy simplifies to the conservation of mechanical energy alone depends on the fluid's characteristics and processes.

Option 2: Isothermal fluid

• When a fluid undergoes an isothermal process, its temperature remains constant throughout the process. This condition implies that the internal energy of the fluid does not change because internal energy for most fluids is predominantly a function of temperature. Since there is no change in internal energy, the energy transformations are limited to mechanical forms, such as kinetic energy and potential energy. In this case, heat transfer occurs to maintain the constant temperature, but it does not contribute to a change in internal energy.

Under these conditions, the conservation of energy principle reduces to the conservation of mechanical energy alone. This is because the fluid's thermodynamic properties do not involve changes in internal energy, and the work done by or on the fluid is directly related to its mechanical energy.

Mathematical Explanation:

For a fluid undergoing an isothermal process, the first law of thermodynamics is expressed as:
Q = W

Here:

• Q = Heat transfer
• W = Work done

Since the internal energy change (ΔU) is zero in an isothermal process, the energy balance simplifies to the work done being equal to the heat transfer. Therefore, the focus shifts solely to the mechanical energy aspects, such as kinetic and potential energy changes, aligning with the conservation of mechanical energy.

Explanation:

Thermodynamic Process of a Balloon Containing an Ideal Gas in an Evacuated and Insulated Room:

• A balloon containing an ideal gas is initially kept in an evacuated and insulated room. The balloon ruptures, and the gas expands to fill the entire room. The process is analyzed to determine which thermodynamic property remains constant or changes.

Key Concepts Involved:

• The room is insulated, implying no heat transfer (Q = 0).
• The system is undergoing free expansion into a vacuum, meaning no work is done (W = 0).
• The gas is ideal, and its behavior follows the ideal gas law.
• In thermodynamics, the internal energy (U) of an ideal gas is a function of temperature and remains constant if there is no heat transfer or work done.

Option 1: Both internal energy and enthalpy of the gas remain constant.

This option is correct because:

• Since the room is insulated, there is no heat exchange (Q = 0).
• The gas is expanding freely into a vacuum, so no work is done on or by the gas (W = 0).
• From the first law of thermodynamics: ΔU = Q - W. In this case, ΔU = 0 - 0 = 0. Therefore, the internal energy (U) of the gas remains constant.
• For an ideal gas, the internal energy (U) depends only on temperature. Since U remains constant, the temperature of the gas remains constant as well.
• Enthalpy (H) for an ideal gas is also a function of temperature: H = U + PV. Since both U and T (and consequently PV) are constant, the enthalpy (H) remains constant as well.

Concept:

The given condition is that PT³ = constant, which implies that the gas is expanding in such a way that the product of pressure and temperature cubed remains constant.

Now, the coefficient of volume expansion (β) is defined as the fractional change in volume per unit change in temperature at constant pressure:

β = (1/V) (∂V/∂T)_P

For an ideal gas, the ideal gas law is given by:

P = (nRT)/V

Taking the differential of PT³ = constant, we get:

P T³ = constant ⟹ P ∝ T^-3

This shows that pressure and temperature have an inverse cubic relationship. The volume of the gas will therefore change in response to temperature changes according to the coefficient of volume expansion.

Calculation:

Given that PT³ is constant, we can conclude that the volume expansion coefficient is proportional to the inverse of the temperature, i.e., β = 4/T.

∴ The correct answer is option 3: 4/T.

Concept:

Intensive and Extensive Properties:

• In thermodynamics, properties of a system are classified into two categories: intensive properties and extensive properties.

Intensive Properties:

• These properties do not depend on the amount of matter present. Examples include temperature, pressure, and density.

Extensive Properties:

• These properties depend on the amount of matter present. Examples include volume, mass, and total energy.

1. Temperature: It is an intensive property because it does not depend on the amount of the substance.
2. Total Volume: It is an extensive property because it depends on the amount of the substance. This means total volume changes with the quantity of the system.
3. Pressure: It is an intensive property because it does not depend on the amount of the substance.
4. Density: It is an intensive property because it does not depend on the amount of the substance. Density is mass per unit volume.

Explanation:

The zeroth law of thermodynamics states that if two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other.

This law is the basis for the temperature measurement.

• By replacing the third body with a thermometer, the Zeroth law can be restated as two bodies are in thermal equilibrium if both have the same temperature reading even if they are not in contact.
• The thermometer is based on the principle of finding the temperature by measuring the thermometric property.

Concept:

If the balloon containing the ideal gas is initially kept in an evacuated and insulated room. Then if the balloon ruptures and the gas fills up the entire room, the process is known as free or unrestrained expansion.

Now if apply the first law of thermodynamics between the initial and final states.

\(Q=(u_2-u_1)+W\)

In this process, no work is done on or by the fluid, since the boundary of the system does not move. No heat flows to or from the fluid since the system is well insulated.

\(u_2-u_1=0\Rightarrow u_2=u_1\)

Enthalpy is given as 

h = u + Pv

For ideal gases, as we know, internal energy and enthalpy are a function of temperature only, so if internal energy U remains constant, temperature T also remains constant which means enthalpy also remains constant.

So, during the free expansion of an ideal gas, both internal energy and enthalpy remain constant.

Concept:

Gibbs phase Rule

P + F = C + Non-compositional variable

If numbers of Non-compositional variable is given then we should put that number, otherwise it is 2

i.e.

P + F = C + 2

P = No. of phases

F = Degrees of freedom

C = No. of components

Calculation:

Given that C = 2, P = 1

P + F = C + 1 (because non-compositional variable is only temperature)

⇒ 1 + F = 2 + 1

Explanation:

Celsius scale 

• In this scale, LFP (ice point) is taken 0° and UFP (steam point) is taken 100°.
• The temperature measured on this scale all in degree Celsius (° C).

Fahrenheit scale 

• This scale of temperature has LFP as 32° F and UFP as 212° F .
• The change in temperature of 1° F corresponds to a change of less than 1° on the Celsius scale.

Kelvin scale 

• The Kelvin temperature scale is also known as the thermodynamic scale. The triple point of water is also selected to be the zero of the scale of temperature.
• The temperatures measured on this scale are in Kelvin (K).

Rankine scale

• This scale of temperature has LPF as 492° R and UFP as 672° R.
• Interval of this scale is according to Fahrenheit.
• The temperature measured on this scale are in Rankine (R)

All these temperatures are related to each other by the following relationship

\(\frac C{100}= \frac {F-32}{180}=\frac {R-492}{180}= \frac {K -273}{100}\)

Additional Information

Relationship between the Celsius and Fahrenheit scale is –

\(\frac{F-32}{9}=\frac{C}{5}\)

\(\Rightarrow C=\frac{5}{9}\left( F-32 \right)\)

Concept:

The volume of the sphere is:

\(V = \frac{4}{3} \times \pi \times {r^3} = \frac{\pi }{6} \times {D^3}\)

D = diameter of the balloon

Calculation:

Given:

Pressure in the balloon (P)

P ∝ D²

P = C × D² … (1)

\(Volume\;of\;a\;sphere = \frac{4}{3} \pi {r^3} = \frac{\pi }{6} {D^3}\)

Now, we can write

V = K × D³

\(D = {\left( {\frac{V}{K}} \right)^{\frac{1}{3}}}\)

Substitute D value in equation (1),

\(P = C \times {\left( {{{\left( {\frac{V}{K}} \right)}^{\frac{1}{3}}}} \right)^2} \Rightarrow P{V^{ - \frac{2}{3}}} = \rm{Constant}\)

Explanation:

According to Zeroth Law, if system A is in thermal equilibrium with system C, and system B is thermal equilibrium with systems C, then system A is in thermal equilibrium with system B.

Now, two systems are said to be in (mutual) thermal equilibrium if, when they are placed in thermal contact (basically, contact that permits the exchange of energy between them), their state variables do not change.

Explanation:

• Intensive Property: These are the properties of the system which are independent of mass under consideration. For e.g. Pressure, Temperature, density, composition, viscosity
• Extensive Properties: The properties which depend on the mass of the system under consideration. For e.g Internal Energy, Enthalpy, Mass, Volume, Entropy

​Important Points

All specific properties are intensive properties. For e.g. specific volume, specific entropy etc.

Concept:

Point function:

• The thermodynamic properties which depend on the end state only (independent of the path followed) are known as point functions like temperature, pressure, density, volume, enthalpy, entropy, etc.

Path function: 

• The thermodynamic properties which depend on the end states, as well as the path followed, are known as path functions like heat and work.

Additional Information

Thermodynamic property: 

• A thermodynamic property is any property that is measurable, and whose value describes a state of a system.
• Some e.g of the thermodynamic property are pressure, temperature, viscosity, and density. 
• Properties are point functions i.e. these do not depend on the path followed. ​

Intensive Property: 

• These are the properties of the system which are independent of the mass under consideration. For e.g. Pressure, Temperature, density, etc.

Extensive Properties:

• The properties which depend on the mass of the system under consideration. For e.g Internal Energy, Enthalpy, Volume, Entropy, etc.

Concept:

The compressibility factor the ratio of actual volume to the volume predicted by the ideal gas law at a given temperature and pressure. It is used to quantify the deviation of real behaviour from the ideal gas behaviour.

\(z = \frac{v}{{\left( {\frac{{RT}}{P}} \right)}} = \frac{{Pv}}{{RT}}\)

Calculation:

Given:

P = 1500 kPa, ν = 2.75 m³/kmol, Z = 0.95, R = 8.314 J/K/mol

Z = \(\frac{Pv}{RT}\)

T = \(\frac{Pv}{RZ}\) =  \(\frac{1500\ \times\ 2.75}{8.314\ \times\ 0.95}\)= 522.26 K \(\approx\) 522 K

T = 522 - 273 = 249 ^∘C 

Additional Information

• For an ideal gas, Z = 1 at all temperatures and pressures.
• Whereas for real gases Z may be > 1 or < 1.
• The farther away Z is from unity, the more the gas deviates from ideal-gas behaviour.

Don't mark 522 K as an answer as the final answer asked is in degree Celcius 249 ∘C.

Explanation:

Temperature: It is the measure of the degree of hotness and coldness of a body. The SI unit of temperature is Kelvin (K).

The major temperature scales are:

• Celsius scale: It is also known as the centigrade scale, and most commonly used scale. It is defined from assigning 0° C to 100° C of freezing and boiling point of water at 1 atmospheric pressure.
• Fahrenheit scale: The temperature scale which is based on 32° for the freezing point of water and 212° for the boiling point of water and the interval between the two range divided into 180 equal parts is called Degree Fahrenheit scale.
• Kelvin scale: It is the base unit of temperature, denoted with K. There are no negative numbers on the Kelvin scale as the lowest is 0 K.

The relation between Celsius and Kelvin is:

°C + 273.15 = K

The relation between degree Fahrenheit and degree Celsius is given by:

\(\frac{{^\circ F - 32}}{9} = \frac{{^\circ C}}{5}\)

Kelvin scale is an absolute scale and it is also known as the absolute thermodynamic scale.

Before 1954 temperature scales were based on two reference points. e.g. Degree Celsius and Fahrenheit scale.

After 1954 the scale and temperature measurement has been based on a single reference point. i.e the Tripple point of water is used as a single reference point.

According to the internationally accepted convention \(1K = ({1\over273.16})\) th of the triple point of water.