Thermodynamics practice · Medium

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.

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 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.

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

Option B ( times and $\sqrt 2$ times) is correct because the mean free path is proportional to temperature and relaxation time is proportional to the square root of temperature.

Option B ($\frac{{{V^2}}}{{4JS}}$) is correct because it correctly relates the increase in temperature to the initial kinetic energy and specific heat, considering the energy conversion efficiency.

Option A (13) is correct because it is the result of integrating the specific heat function over the given temperature range.

Option A (Both (A) and (R) are true and (R) is the correct explanation of (A)) is correct because in an isobaric process, as heat is added, the temperature increases, leading to an increase in volume, and this is because the heat is used for both internal energy increase and work done.

Option A (Gas constant (R)) is correct because the gas constant is a fixed value, not a thermodynamic coordinate which can vary.

Option B (Heat is a path function, while internal energy is not) is correct because heat transfer depends on the process, while internal energy depends only on the state of the system.

Option A is correct because it represents the increase in temperature due to the rotational kinetic energy being converted into heat energy when the Earth stops rotating.

Option C ($\frac{{\gamma + 1}}{2}$ ) is correct because the average time of collision increases with volume as $V^{(\gamma+1)/2}$ in an adiabatic expansion.

Option C (A mixture of monoatomic and diatomic gases) is correct because a gamma value of 1.5 lies between the gamma values of monoatomic (1.67) and diatomic (1.4) gases, implying a mixture.

Option B (8900 J) is correct because it is the change in internal energy calculated using the first law of thermodynamics: $\Delta U = Q - W$.

Option D (${T_p} > {T_Q}$) is correct because for a real gas, the difference between Cp and Cv decreases as temperature decreases.

Option B (Of its high specific heat) is correct because water's high specific heat capacity allows it to absorb a large amount of heat without a significant temperature increase, making it an effective coolant.

This statement describes the zeroth law of thermodynamics, which states that if two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. Therefore, the statement is true.

The Assertion is correct because the heat given to the gas depends on the path taken (first law of thermodynamics). The Reason is incorrect because heat is a path function, not a state function.