Thermodynamics practice · Mixed difficulty

Option D is correct because, by definition, an adiabatic process is one in which there is no heat exchange between the system and its surroundings, meaning the total amount of heat remains constant.

Option A (${C_V} = 3,\;{C_P} = 5$) is the most reliable because the difference between $C_P$ and $C_V$ should be approximately equal to R (approximately 2 cal/mol-K).

The change in entropy is $+ 4.5cal/K$ because it is calculated by dividing the heat absorbed by the ice during melting by the temperature at which melting occurs.

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 B is correct because the first law of thermodynamics is a statement of the conservation of energy, stating that energy cannot be created or destroyed, only transformed.

Option B (Law of conservation of energy) is correct because the first law of thermodynamics is a specific application of the law of conservation of energy.

Option A is correct because the work done by a gas expanding at constant pressure is given by the formula $W = P(V_2 - V_1)$, where P is the constant pressure, V2 is the final volume, and V1 is the initial volume.

When heat is absorbed by a gas, the entropy increases because the gas molecules have more energy and can move in more disordered ways. Therefore, the change in entropy is positive.

Option D is correct because the specific heat of an ideal gas is constant and does not vary with temperature, hence it is proportional to $T^0$.

The value of ${W_4}$ is $150J$ because the net heat involved in a cyclic process equals the net work done.

Option B (Decreases with increasing pressure) is correct because ice is one of the few substances that contracts upon melting, so increasing pressure favors the liquid phase, lowering the melting point.

Option D (600 K) is correct because it is the intake temperature calculated using the Carnot engine efficiency formula.

Option B ($\infty$) is correct because during a phase change, the temperature remains constant, requiring infinite heat for a finite temperature change, hence infinite specific heat.

Option A (210 s) is correct because it is the time required to convert 100g of water at 100°C to steam, calculated using the latent heat of vaporization and the power of the heater.

Option B (${C_p} - {C_V}$) is correct because the universal gas constant is defined as the difference between the specific heat at constant pressure and the specific heat at constant volume.

Option C ($\frac{5}{3}$) is correct because the coefficient of performance (COP) for a refrigerator is the ratio of heat absorbed from the cold reservoir to the work done.

The potential energy of the water at the top of the waterfall is converted into kinetic energy, which is then converted into heat. Using the formula $mgh = mc\Delta T$, we can solve for the change in temperature, which is approximately 0.23°C.

Option C (Assertion is true but Reason is false) is correct because the ratio of specific heats is indeed lower for monatomic gases, but this is because monatomic gases have *fewer* degrees of freedom.

Option D (Adiabatic) is correct because an adiabatic process is defined as one where no heat is exchanged with the surroundings.

Option B is correct because decreasing the sink temperature has a greater impact on efficiency than increasing the source temperature, especially at lower temperatures.

Option A ($\frac{{11}}{8}T$) is correct because the equilibrium temperature is found by equating the total internal energy before and after mixing.

Option D (300 R ln 2) is correct because the work done in an isothermal process is given by $W = -nRT \ln(\frac{{V_2}}{{V_1}})$ and since the pressure doubles, the volume halves.

Option B (Heat) is correct because an adiabatic process is defined as a thermodynamic process in which there is no heat transfer into or out of the system.

Option A (${T_1}V_1^{\gamma - 1} = {T_2}V_2^{\gamma - 1}$) is correct because this equation represents the relationship between temperature and volume in an adiabatic process.

Option B ($1.40$) is correct because the ratio of specific heats (${C_P}/{C_V}$) for diatomic molecules is approximately 1.40.

Option C ($1.75\mathrm{kg}{\mathrm{m}^{ - 3}}$) is correct because the density is calculated using the gas constant, the difference between specific heats, and the ideal gas law.

The change in internal energy is calculated using the formula $\Delta U = mc_v\Delta T$. Substituting the given values, we get $\Delta U = 0.08 \times 0.17 \times 5 \times 4186.8 \approx 284 J$.

Option A ($6.19 \times 10^5 \mathrm{~N} / \mathrm{m}^2$) is correct because the final pressure is calculated using the adiabatic process equation, $P_1V_1^\gamma = P_2V_2^\gamma$, where $\gamma = C_p/C_v$.

Option A is correct because in an adiabatic process, no heat is exchanged with the surroundings (Q=0), so the work done is equal to the negative change in internal energy (W = -ΔU), making it path-independent.

Option C (7, 5) is correct because the difference between the two specific heats should be close to R (approximately 2 cal/mol K).