Thermodynamics practice · Medium

Option B ($( {1 + \frac{{2}}{f}} )$) is correct because it represents the correct relationship between the ratio of specific heats and the degrees of freedom.

Option C ($\frac{1}{{{n^{\gamma - 1}}}}$) is correct because it is derived from the ratio of pressures calculated under isothermal and adiabatic conditions.

Option B is correct because in an adiabatic process, there is no heat exchange with the surroundings, meaning the work done equals the negative change in internal energy.

Option D is correct. For an isolated system, mechanical energy can be conserved if only conservative forces are acting, and internal energy is not always constant due to processes like friction.

Option C (Pressure, volume and temperature) is correct because these three variables are sufficient to define the state of a thermodynamic system in equilibrium.

Option C is correct because the assertion is true about adiabatic processes, but the reason is false as temperature changes in an adiabatic process.

Option C (1.56) is correct because it is calculated using the formula for the equivalent value of $\gamma$ for a mixture of gases, considering the number of moles and degrees of freedom of each gas.

Option A ($\Delta T=\frac{\omega^2 R^2}{5 J s}$) is correct because the increase in temperature is calculated by equating the rotational kinetic energy to the heat energy gained.

Option A (Disorder of molecular motion of the system) is correct because entropy is a measure of the randomness or disorder of a system at the molecular level.

Option A ($\Delta U = - W$ in an adiabatic process) is correct because in an adiabatic process, there is no heat exchange, so the change in internal energy is equal to the negative of the work done by the system.

Option A ($\sqrt{\frac{\pi}{6}}: 1$) is correct because it represents the ratio of initial cooling rates based on surface area to mass ratio.

Option B (25 J) is correct because the heat absorbed is calculated using the first law of thermodynamics, considering both the change in internal energy and the work done.

Option D (Any one of pressure, volume or temperature) is correct because a single thermodynamic variable is insufficient to define the state of the system.

Option B (Decreases) is correct because the conversion of water to ice results in a more ordered state, thus reducing entropy.

Option A (If both assertion and reason are true and reason is the correct explanation of assertion) is correct because the zeroth law defines thermal equilibrium, and temperature is the physical quantity that is the same for systems in thermal equilibrium.

Option A (Both (A) and (R) are true and (R) is the correct explanation of (A)) is correct because the fog formation is due to the adiabatic expansion of the gas, which causes cooling and condensation.

Option B (Tangent law) is correct because deflection magnetometers operate based on the tangent law, which relates the magnetic field components.

Option A (0.4) is correct because the efficiency of a heat engine is calculated using the formula $\eta = 1 - \frac{{T_2}}{{T_1}}$ with temperatures in Kelvin.

Option A ($n R T \log _e\left(\frac{V_2-n \beta}{V_1-n \beta}\right)+\alpha n^2\left(\frac{V_1-V_2}{V_1 V_2}\right)$) is correct because it is the work done calculated by integrating the pressure from the van der Waals equation over the volume change.

Option D (Both (2) and (3) are correct) is correct because in an isothermal expansion of an ideal gas, the internal energy remains constant, and the heat absorbed equals the work done.

Option D (If both Assertion & Reason are false) is correct because the COP of a refrigerator can be greater than unity, and the reason provided is not universally true for all refrigerators.

Option D (1000 J) is correct because the external work done during expansion at constant pressure is calculated using $W = P\Delta V$.

Option A (If both Assertion and Reason are correct and Reason is the correct explanation of Assertion) is correct because the volume decreases during melting, and the work done by the surroundings is positive.

Option B (4320) is correct because 90% of the heat is used to increase the internal energy after accounting for the expansion work.

Option C ($n p$) is correct because the bulk modulus for a process $pV^n = constant$ is given by $n p$.

Option C ($\left(\frac{3}{2}\right) n R T_0$) is correct because the work done is calculated by integrating p dV, using the given temperature-volume relationship.

Option A (Statement-I is true and statement-II is true) is correct because reversible systems are indeed difficult to find due to the dissipative nature of most real-world processes.

Option B (The slope of adiabatic is more than that of isothermal) is correct because the adiabatic curve is steeper than the isothermal curve, as the ratio of slopes is given by γ > 1.

Option B (Wave nature of electron) is correct because the Davisson-Germer experiment demonstrated the diffraction of electrons, confirming their wave-like properties.

Option C is correct. The first law of thermodynamics describes energy conservation, not the conditions for heat to work conversion. The second law correctly states that heat flows spontaneously from hot to cold bodies.