A balloon containing an ideal gas is initially kept in an evacuated and insulated room. The balloon ruptures and the gas fills up the entire room. Which one of the following statements is TRUE at the end of above process ?
The internal energy of the gas decreases from its initial value, but the enthalpy remains constant
The internal energy of the gas increases from its initial value, but the enthalpy remains constant
Both internal energy and enthalpy of the gas remain constant
Both internal energy and enthalpy of the gas increase
Answer (Detailed Solution Below)
Option 3 : Both internal energy and enthalpy of the gas remain constant
Thermodynamics System and Processes MCQ Question 1 Detailed Solution
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.
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.
In case of mixing of water and sulphuric acid, the enormous amount of heat is released as mixing is highly exothermic. So there is no more any thermal equilibrium. So Zeroth Law is not valid.
A 100 W electric bulb was switched in a 2.5 m × 3 m × 3 m size thermally insulated room having a temperature of 20°C. The room temperature at the end of 24 hours will be ______. (Take ρ of air at atmospheric temperature and pressure = 1.2 kg/m3).
321°C
341°C
450°C
470°C
Answer (Detailed Solution Below)
Option 4 : 470°C
Thermodynamics System and Processes MCQ Question 3 Detailed Solution
In a two component system, if the non-compositional variable is only temperature, the number of degrees of freedom in the case of a single phase field as per Gibbs Phase Rule is?
0
1
2
3
Answer (Detailed Solution Below)
Option 3 : 2
Thermodynamics System and Processes MCQ Question 4 Detailed Solution
A reversible thermodynamic cycle containing only three processes and producing work is to be constructed. The constraints are: (a) there must be one isothermal process, (b) there must be one isentropic process, (c) the maximum and minimum cycle pressures and the clearance volumes are fixed, and (d) polytropic processes are not allowed. Then the numbers of possible cycles are
1
2
3
4
Answer (Detailed Solution Below)
Option 4 : 4
Thermodynamics System and Processes MCQ Question 5 Detailed Solution
n = 0 ⇒ P = C ⇒ Constant Pressure Process (Isobaric Process)
n = 1 ⇒ PV = C ⇒ Constant Temperature Process (Isothermal process)
n = γ ⇒ PVγ = C ⇒ Adiabatic Process
n = ∞ ⇒ V = C ⇒ Constant Volume Process (Isochoric process)
According to the question:
The constraints are: (a) there must be one isothermal process, (b) there must be one isentropic process, (c) the maximum and minimum cycle pressures and the clearance volumes are fixed, and (d) polytropic processes are not allowed.
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.
A mercury thermometer was first placed in melting ice and the length of mercury column was observed to be 10 mm; when it was placed in steam, the length of the column was 250 mm. When placed in tap water, the length of the column was 58 mm. The temperature of the tap water is
24.2°C
20°C
38.4°C
4.14°C
Answer (Detailed Solution Below)
Option 2 : 20°C
Thermodynamics System and Processes MCQ Question 7 Detailed Solution
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
A body of mass 20 kg falls freely in vacuum. It has fallen through a vertical distance of 50 m. The gravitational acceleration may be assumed as 10 m/s^{2}. What is the thermodynamic work done by the body?
1000 Nm
10 kJ
0
1 kNm
Answer (Detailed Solution Below)
Option 3 : 0
Thermodynamics System and Processes MCQ Question 9 Detailed Solution
Work done by a body depends on the medium in which the body is falling in.
If a body is falling in vacuum there will be no resistance to the body hence there will be no work done. i.e. W = 0
If a body is falling in atmosphere work done will be product of mass of the body (m) height the body is falling from (z) , gravitational acceleration(g) i.e. W = mgz
The state of a system in which properties are definite as long as external conditions are unchanged is called an equilibrium state.
Thermodynamic equilibrium:
The system is said to be in thermodynamic equilibrium if the conditions for the following three equilibrium is satisfied:
1) Mechanical equilibrium:
When there are no unbalanced forces within the system and between the system and the surrounding, the system is said to be under mechanical equilibrium.
This means that the pressure of the system is constant everywhere.
2) Chemical equilibrium:
The system is said to be in chemical equilibrium when there are no chemical reactions going on within the system or there is no transfer of matter from one part of the system to other due to diffusion.
3) Thermal equilibrium:
When the temperature of the system is uniform and not changing throughout the system and also in the surroundings, the system is said to be in thermal equilibrium.
This means that the temperature of the system is constant everywhere.
A system is said to be in thermodynamic equilibrium if it is simultaneously in mechanical, thermal, and chemical equilibrium.
Therefore, thermodynamic equilibrium is completely defined by the specification of internal energy (since it is a function of temperature only), enthalpy (enthalpy (H) = Internal energy (U) + PV), and generalized displacements (i.e. due to unbalanced forces).
Path functions are defined as the thermodynamical variables which depend on the way/path in which the thermodynamical system achieved the initial and final states.
The differential of path functions is inexact.
Heat, work and entropy generation are path functions.
Point functions:
Point functions are defined as the thermodynamic variable which depends on end states only i.e. initial and final states. They do not depend upon path followed.
The differential of point functions is exact.
Pressure, temperature, volume, entropy, enthalpy, energy etc are point functions.
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.
The pressure inside a balloon is proportional to the square of its diameter. It contains 2 kg of water at 150 kPa with 85% quality. The balloon and water are now heated so that a final pressure of 600 kPa is reached. The process undergone by the water is given by p-v equation as:
In thermodynamics, a process in which the system undergoes a succession of equilibrium states is a
1) Quasi-static process
2) Reversible process
3) Irreversible process
4) Path independent process
1 & 3
1 & 2
3 & 4
2 & 4
Answer (Detailed Solution Below)
Option 2 : 1 & 2
Thermodynamics System and Processes MCQ Question 14 Detailed Solution
A quasi-static process is a process in which the state variables of a thermodynamical system change infinitely slowly, thus the system appears nearly static.
It is a hypothetical and ideal process which is reversible and experiences thermodynamic equilibrium at every stage of the process.
A quasi-static process can be assumed to be a Reversible process.
Following points are important regarding Reversible and Irreversible process.
Reversible Processes
A thermodynamic process driving from initial state to final state is said to be reversible, if the system as well as its surrounding returns back to its initial state, without any change in the universe.
The processes which can be idealized as reversible are Motion without friction, Expansion/ compression with infinitesimal pressure difference, Energy transfer as heat with infinitesimal temperature difference.
Irreversible Processes
A thermodynamic process that does not return back to its initial state is termed as an irreversible process.
The examples of irreversible processes are Motion with friction, free expansion, Expansion/ compression with finite pressure difference, Energy transfer as heat with finite, mixing of matter at different states, Mixing of non-identical gases.
Work done by a closed system in an adiabatic process is equal to the internal energy, which is a point function. Also in the case of an adiabatic process for a closed system work is independent of path.
Joule-Kelvin Effect:
A graph is made where a gas temperature is recorded at different pressure keeping enthalpy constant.
A series of the experiment is done with different enthalpy values and temperature, pressure is recorded.
The curve passing through the maxima of these enthalpies is called the inversion curve.
Inversion Curve:
The numerical value of the slope at any point is called the Joule-Kelvin coefficient (μ_{J}).
The curve passing through the maximum temperature in different enthalpies in the temperature-pressure graph is known as Inversion Curve. It is the locus of all points where μ_{J }is zero.
μ_{J}
Effect
Positive
Cooling region
Negative
Heating region
0
Only for an ideal gas.
A liquid expands upon freezing when the slope of its fusion curve on the pressure-temperature diagram is negative.
Reversible process: A thermodynamic process driving from initial state to final state is said to be reversible, if the system as well as its surrounding returns back to its initial state, without any change in the universe.
Eg. Frictionless pendulum, quasi-static expansion and compression of a gas.
Irreversible process: A thermodynamic process driving from initial state to final state is said to be irreversible, if the system as well as its surroundings do not return back to its initial state or return back with some change in the universe.
Eg. any natural process carried out with a finite gradient is an irreversible process, ∴ heat engine and internal combustion engine are irreversible devices.
Frictionless pendulum:
It is possible for a simple pendulum to oscillate for an infinite time if friction is not present. It does not violate any law of thermodynamics.
A perpetual frictionless pendulum is a reversible process where net heat and net-work exchange between the system and the surroundings is zero.
Heat transfer is defined as the form of energy that is transferred between two systems or a system and its surroundings by virtue of a temperature difference.
it is the area under the process curve on a T-S diagram during an internally reversible process
this area has no meaning for irreversible processes.
From the definition of entropy,v we know that heat flow in an internally reversible process is dQ = TdS
where dQ corresponds to the differential area on T-S diagram
Total heat transfer from an internally reversible process is Q = \(\int TdS\)