Thermodynamics practice · Mixed difficulty

Option A ($9R$) is correct because, according to the equipartition theorem, each atom in a water molecule contributes 3R to the molar heat capacity, and a water molecule has 3 atoms.

Option C (Minimum for $n=0$) is correct because the work done is minimum for isobaric process where n=0.

Option B ($J/kg{\;^0}C$) is correct because specific heat is defined as the amount of heat required to raise the temperature of 1 kg of a substance by 1 degree Celsius.

Option A ($\Delta {U_1} = \Delta {U_2}$) is correct because the change in internal energy is a state function and depends only on the initial and final states, not the path taken.

Option D (Adiabatic) is correct because an adiabatic process is defined as one in which no heat is exchanged between the system and its surroundings.

The correct answer is C (Temperature of system may decrease inspite of heat is being absorbed by the system) because if the system does work while absorbing heat, its internal energy and thus temperature can decrease.

Option D (1000 K) is correct because it is calculated by first finding the temperature of the sink using the initial efficiency and source temperature, and then using the new efficiency and the same sink temperature to find the new source temperature.

Option B (Adiabatic compression) is correct because in adiabatic compression, work is done on the gas, increasing its internal energy.

Option D (If Assertion is false but the Reason is true) is correct because the first law of thermodynamics applies to all systems, not just ideal gases, and it is indeed a statement of energy conservation.

Option C (decreases) is correct because when water freezes into ice, it becomes more ordered, thus decreasing entropy.

Option B is correct because in an isothermal expansion, the pressure is inversely proportional to the volume, and compressibility is the measure of the change in volume with pressure.

Option B is correct because for an isothermal process, the relationship between pressure and volume changes can be derived from the ideal gas law.

Option A ($27 \times {10^5}N/{M^2}$) is correct because it follows from the adiabatic condition equation relating pressure and temperature.

Option C (02-Mar) is correct because the efficiency of a Carnot engine is calculated using the temperatures of the hot and cold reservoirs.

Option A is correct because the free expansion into a vacuum is an adiabatic process with no work done, resulting in no temperature change.

Option C ($- \frac{{\Delta p}}{{\mathrm{\gamma }p}}$) is correct because it is derived from the adiabatic process equation relating pressure and volume changes.

The correct answer is C (If assertion is true, but reason is false) because the first law of thermodynamics is indeed a restatement of the principle of conservation of energy, but energy being a fundamental quantity is not the correct reason.

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 A ($350 \mathrm{~J}$) is correct because for an isobaric process, the heat given to the gas is calculated using $Q = \Delta U + W$, where $\Delta U = \frac{f}{2} nR \Delta T$ and $W = nR \Delta T$. For a diatomic gas, $f = 5$.

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 ($\frac{n}{n+2}$) is correct because it represents the ratio of specific heat at constant volume to specific heat at constant pressure for a gas with n degrees of freedom.

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.