Assertion (A): Energy of molecules increase on increasing the temperature.
Reason (R): All substances expand on increasing the temperature.
Concept: Temperature is a measure of average kinetic energy. Thermal expansion.
Formula: Average Kinetic Energy \( \propto T \).
Solution: Increasing temperature increases molecular kinetic energy. However, not all substances expand on heating (e.2.g., water between \( 0^{\circ}\text{C} \) and \( 4^{\circ}\text{C} \)). So R is false.
Assertion (A): Work done by a gas in isothermal expansion is more than the work done by the gas in the same expansion adiabatically.
Reason (R): Temperature remains constant in isothermal expansion but not in adiabatic expansion.
Concept: Work done is area under P-V curve. Isothermal vs. Adiabatic expansion.
Formula: \( W = \int P dV \). Isothermal: \( PV = \text{constant} \). Adiabatic: \( PV^{\gamma} = \text{constant} \), where \( \gamma > 1 \).
Solution: During expansion from the same initial state to the same final volume, the pressure in isothermal process drops slower than in adiabatic process, leading to more work done. Temperature remains constant in isothermal and changes in adiabatic.
Assertion (A): During free expansion of an Ideal gas, entropy is zero.
Reason (R): Internal energy of an ideal gas is zero during free expansion.
Concept: Free expansion of an ideal gas. Entropy change. Internal energy.
Formula: For ideal gas, \( \Delta U = 0 \) (as \( Q=0, W=0 \)). Entropy change \( \Delta S > 0 \) for irreversible free expansion.
Solution: During free expansion of an ideal gas, \( \Delta U = 0 \) (meaning \( T \) is constant), but the internal energy itself is not zero. Also, free expansion is irreversible, so entropy *increases* (not zero). Both A and R are false.
Assertion (A): In an ideal monoatomic gas, The Internal energy of gas is equal to translational Kinetic energy of all its molecules
Reason (R): The Internal energy may get contributes from Translational, Rotatory, vibrationally as well as from the Potential energy corresponding to the molecular force.
Concept: Internal energy components for different types of gases.
Formula: For monoatomic ideal gas, \( U = \frac{3}{2} nRT \) (translational only).
Solution: For an ideal monoatomic gas, internal energy is purely translational kinetic energy. General internal energy can have translational, rotational, vibrational, and potential contributions (for real/complex gases), but potential energy is zero for ideal gases. A is true, R is true but not an explanation for A.
Assertion (A): For gas molecules absolute zero temperature is not the temperature of zero energy.
Reason (R): Only the kinetic energy of the molecules is represented by temperature.
Concept: Temperature and molecular energy. Temperature is a direct measure of the average translational kinetic energy of molecules. While kinetic energy is minimal at 0 K, gas molecules can still have potential energy from intermolecular interactions. Thus,0 K is not zero total energy. Both (A) and (R) are true, and (R) explains (A).
Reason (R): On sudden expansion, no heat is supplied to system and hence gas does work at the expense of its internal energy.
Concept: Adiabatic expansion and First Law of Thermodynamics. Sudden expansion is a rapid process, approximated as adiabatic (( Q = 0 )). The gas does work ( W > 0 ). By \( \Delta U = Q - W ), ( \Delta U \) becomes negative, leading to a decrease in internal energy and thus cooling. Both (A) and (R) are true, and (R) explains (A).
Assertion (A): Bursting of balloon is not a equilibrium state.
Reason (R): Equilibrium state of a thermodynamic system is completely described by specific values of some macroscopic properties.
Concept: Thermodynamic equilibrium. A bursting balloon is a spontaneous, non-equilibrium process. An equilibrium state is characterized by constant macroscopic properties. Both assertion (A) and reason (R) are true, and (R) correctly explains (A).
Assertion (A): Work and heat both can be converted into each other in any condition.
Reason (R): Work and Heat both are different form of energy.
Concept: First Law of Thermodynamics and nature of work/heat. Work and heat are forms of energy transfer, not different forms of energy itself. Their interconversion is governed by thermodynamic laws and not possible under 'any condition'. Both (A) and (R) are false.
Assertion (A): If volume of a gas is increasing but temperature of the gas is decreasing, then heat given to the gas may be positive, negative or zero.
Reason (R): Heat given to a gas is a path function, it is not a state function.
Concept: First Law of Thermodynamics (( Delta U = Q - W )). If volume increases, (W > 0) (work done by gas). If temperature decreases, ( Delta U < 0 ). So, ( Q = Delta U + W ) can be positive, negative, or zero. Heat is indeed a path function. Both (A) and (R) are true, and (R) explains (A).
Assertion (A): Molar heat capacity of a gas in any process can have any value ( -infty ) to ( +infty ).
Reason (R): Molar heat capacity of a gas in an isothermal process is ( infty ).
Concept: Molar heat capacity \( C = \frac{dQ}{dT} \). For an isothermal process, ( dT = 0 ), so ( C = infty ). For an adiabatic process, ( dQ = 0 ), so ( C = 0 ). Thus, molar heat capacity can range from ( -infty ) to ( +infty ). Both (A) and (R) are true, and (R) explains (A).