If the internal energy of an ideal gas drops by an amount equal to the work it performs, the type of process is called ………
(A) cyclic
(B) isothermal
(C) adiabatic
(D) isochoric
Explanation: The question deals with thermodynamic processes in an ideal gas where internal energy and work done are related through energy conservation principles. In Thermodynamics, the internal energy of an ideal gas depends only on temperature, and any change in it is governed by how Heat and work interact within the system. A process is defined based on which variables remain constant or how energy transfer occurs between system and surroundings.
In this situation, the system is performing work while its internal energy decreases by the same amount, meaning there is no NETHeat exchange with the surroundings. This condition represents a special thermodynamic case where energy lost internally is completely converted into external work without Heat flow. Such behavior is characteristic of a process where Heat transfer is absent and energy transformation is purely mechanical in nature.
When analyzing thermodynamic processes, one must consider whether Heat is added or removed, whether volume or pressure changes, and how internal energy responds. The relationship between Heat, work, and internal energy is governed by the first law of Thermodynamics, which states that energy is conserved in all transformations within a closed system.
Overall, the situation describes a purely energy-conversion-driven transformation where internal energy change is entirely accounted for by work done by the system, indicating a distinct thermodynamic process category.
Option c – adiabatic
A gas releases 50 J of Heat during cooling and compresses in such a way that 20 J of work is done on it. What is the resulting change in internal energy?
(A) 70 J
(B) -30 J
(C) 30 J
(D) -70 J
Explanation: This question is based on the first law of Thermodynamics, which connects Heat transfer, work done, and internal energy change in a system. Heat released by a system is considered negative, while work done on the system is taken as positive. These sign conventions are essential for correctly analyzing energy changes in thermodynamic processes.
Here, the gas is cooling, meaning it loses energy in the form of Heat to its surroundings. At the same time, the system is being compressed, which means external work is being done on the gas, increasing its internal energy. Both effects must be combined algebraically to determine the NET change in internal energy.
The process involves carefully balancing energy loss due to heat release and energy gain due to compression work. Heat transfer reduces internal energy, while work done on the system increases it. The final internal energy change depends on which effect dominates after applying the correct signs and summing both contributions.
Such problems are common in Thermodynamics because they test understanding of energy flow direction and sign conventions rather than direct computation alone. The key is consistently applying the first law framework to track how energy enters and leaves the system through heat and work interactions.
Overall, the change in internal energy results from the combined effect of heat loss and mechanical work input during compression.
Option b – -30 J
Which statement accurately describes entropy?
(A) The entropy of a flawless crystal at 0 °C is assumed to be zero
(B) A perfect crystal has some entropy at absolute zero temperature
(C) All crystals are assumed to have zero entropy at absolute zero
(D) A perfect crystal has zero entropy at absolute zero temperature
Explanation: Entropy is a thermodynamic property that measures the degree of randomness or disorder in a system and is closely linked with energy dispersal. It is a state function, meaning its value depends only on the current state of the system and not on the path taken to reach that state. In Thermodynamics, entropy plays a central role in determining the direction of spontaneous processes.
At very low temperatures, especially near absolute zero, the behavior of crystalline substances becomes highly ordered. A perfect crystal is assumed to have atoms arranged in a completely regular pattern with minimal disorder. According to thermodynamic principles, entropy approaches its minimum value under such ideal conditions. However, real substances may still have slight imperfections or residual disorder, affecting their entropy.
When evaluating entropy-related statements, it is important to distinguish between ideal theoretical assumptions and real physical behavior. The third law of Thermodynamics provides a foundation for understanding entropy at absolute zero, stating how entropy behaves in perfectly ordered systems under ideal conditions.
Overall, the concept focuses on how Molecular disorder changes with temperature and structural arrangement, especially in highly ordered systems at extremely low temperatures.
Option d – A perfect crystal has zero entropy at absolute zero temperature
The neutralization of NaOH with HCl releases 57.1 kJ/mol of heat. If 0.28 moles of each are reacted, how much heat is liberated?
(A) 16 kJ
(B) 14.5 kJ
(C) 18 kJ
(D) 26.2 kJ
Explanation: This question is based on the concept of enthalpy change during a neutralization reaction, which is an exothermic process where Acid and Base react to form water and Salt. The heat released per mole of reaction is constant for a given strong Acid–strong Base combination under standard conditions.
In such reactions, the total heat evolved depends directly on the number of moles reacting. Since enthalpy change is given per mole, scaling it according to the actual amount of reactants allows calculation of total heat released. This proportional relationship is essential in thermochemistry.
Neutralization reactions typically involve complete ionization of strong Acids and Bases in aqueous solution, leading to the formation of water molecules and release of energy due to bond formation. The heat released is a direct measure of the energy difference between reactants and products.
To determine the total heat liberated, the molar enthalpy change is multiplied by the number of moles participating in the reaction. Careful attention must be given to stoichiometric equivalence when both reactants are present in equal amounts.
Overall, the process reflects energy release proportional to the extent of reaction between Acid and Base in aqueous solution.
Option a – 16 kJ
Which of the following is classified as an intensive property?
(A) specific heat capacity
(B) entropy
(C) internal energy
(D) enthalpy
Explanation: In Thermodynamics, properties of a system are divided into intensive and extensive categories based on whether they depend on the amount of substance present. Intensive properties remain unchanged regardless of system size, while extensive properties vary directly with the amount of Matter.
Understanding this distinction is important in analyzing physical and chemical systems. Intensive properties describe the state of a system independently of its Mass or volume, whereas extensive properties scale with system size. This classification helps in comparing different systems and understanding their intrinsic characteristics.
Examples of intensive properties include temperature, pressure, density, and specific quantities that are independent of system scale. Extensive properties include Mass, volume, internal energy, and enthalpy, which depend on how much material is present.
When evaluating options, one must identify which property remains invariant even if the system is divided into smaller parts. Such properties reflect inherent characteristics of the substance rather than its quantity.
Overall, the concept focuses on distinguishing size-independent physical properties from those that depend on the amount of Matter in the system.
Option a – specific heat capacity
When 1 mole of Al₄C₃(s) reacts with water in a sealed container at 27 °C under atmospheric pressure, what is the amount of work done?
(A) -1800 cal
(B) -600 cal
(C) +1800 cal
(D) zero cal
Explanation: This question involves thermodynamic work associated with chemical reactions occurring in a system where gases may be produced. Work in thermodynamics is often related to expansion or compression against external pressure, especially when gases are formed or consumed.
In a sealed container under constant atmospheric pressure, work done by or on the system depends on volume change. If gaseous products are formed, expansion work is performed by the system; if no volume change occurs, the work is zero. The nature of reactants and products determines whether any significant expansion takes place.
Reactions involving Solid reactants and aqueous conditions may or may not produce gases. The presence or absence of gas Evolution is crucial in determining whether the system performs pressure–volume work. If no NET gas expansion occurs, no work is done against the surroundings.
Thermodynamic work is calculated using pressure–volume relationships, but in simplified conceptual Questions, identifying whether expansion occurs is sufficient. The sealed container condition ensures controlled pressure, making analysis more straightforward.
Overall, the work depends on whether the reaction produces a change in volume due to gas formation or remains confined without expansion.
Option d – zero cal
During which of the following processes does the temperature drop?
(A) adiabatic compression
(B) isothermal expansion
(C) isothermal compression
(D) adiabatic expansion
Explanation: This question is related to thermodynamic processes such as adiabatic and isothermal changes, where temperature behavior depends on how heat and work are exchanged. In different processes, temperature may remain constant, increase, or decrease depending on energy transfer conditions.
In adiabatic processes, no heat is exchanged with the surroundings. Therefore, any change in internal energy comes entirely from work done by or on the system. When a gas expands adiabatically, it uses its internal energy to perform work, leading to a decrease in temperature. Conversely, compression increases temperature due to work done on the gas.
In isothermal processes, temperature remains constant because heat exchange exactly balances work done. Therefore, no temperature drop occurs in such cases. Understanding this distinction is essential in identifying how energy transformations affect temperature.
The key factor is whether the system loses internal energy without receiving heat input. Expansion against external pressure in an insulated system results in cooling, as energy is consumed in doing work.
Overall, temperature decrease occurs in processes where internal energy is used for expansion work without heat supply from the surroundings.
Option d – adiabatic expansion
A system absorbs 60 J of heat and performs 245 J of work on its surroundings. What is the change in its internal energy?
(A) 90 J
(B) -185 J
(C) -180 J
(D) 225 J
Explanation: This question is based on the first law of thermodynamics, which relates heat added to a system, work done by the system, and the resulting change in internal energy. The law ensures energy conservation in thermodynamic processes.
When a system absorbs heat, its internal energy tends to increase. However, if the system simultaneously performs work on its surroundings, it loses energy. The NET change in internal energy depends on the balance between energy gained through heat and energy lost through work.
Sign conventions are crucial: heat absorbed is positive, while work done by the system is considered positive in terms of energy leaving the system. The internal energy change is calculated by subtracting work done from heat absorbed.
This type of problem emphasizes understanding energy flow rather than computation alone. It highlights how systems can gain and lose energy simultaneously through different mechanisms.
Overall, internal energy change results from the competition between heat intake and work output in the system.
Option b – -185 J
In which of the following cases is the change in entropy negative?
(A) iodine undergoing sublimation
(B) hydrogen molecules dissociating
(C) formation of liquid water
(D) decomposition of calcium carbonate
Explanation: Entropy change is associated with the degree of disorder or randomness in a system during physical or chemical processes. A negative entropy change indicates that the system becomes more ordered, meaning randomness decreases.
Processes that involve gas formation typically increase entropy, while those involving phase transitions from gas to liquid or liquid to Solid decrease entropy. Similarly, decomposition reactions often increase entropy due to formation of more particles, whereas combination reactions may decrease entropy.
When evaluating entropy change, one must consider the direction of Molecular organization. If particles become more structured or confined, entropy decreases. If they become more dispersed or free to move, entropy increases.
Phase changes such as condensation or freezing typically reduce entropy because molecules lose freedom of movement and become more ordered. chemical reactions that reduce the number of gaseous molecules also lead to lower entropy.
Overall, entropy decreases when a system transitions to a more ordered state with reduced Molecular randomness.
Option c – formation of liquid water
Which of the following are not considered state functions? i. q + w ii. q iii. w iv. H – TS
(A) Only i, ii, and iii
(B) Only ii and iii
(C) Only i and iv
(D) Only ii, iii, and iv
Explanation: State functions depend only on the current state of a system and not on the path taken to reach that state, whereas path functions depend on the specific process followed. Identifying state functions is essential in thermodynamics for analyzing system behavior.
Heat (q) and work (w) are path functions because their values depend on how a process occurs rather than just initial and final states. However, combinations of thermodynamic quantities can sometimes form state functions, depending on their mathematical definitions.
Expressions involving internal energy, enthalpy, and Gibbs free energy are state functions because they are defined in terms of state variables. In contrast, heat and work individually do not qualify as state functions. However, certain combinations may or may not retain path dependence depending on their formulation.
Understanding this distinction helps in applying the first law of thermodynamics correctly, where internal energy change is a state function, while heat and work are process-dependent quantities.
Overall, identifying whether a quantity depends on state or path is crucial in classifying thermodynamic variables.
Option b – Only ii and iii
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