According to the Clausius inequality, for a cyclic process involving heat transfer between a system and its surroundings at a single constant temperature (T), the following inequality must hold true:

Correct Answer: D

Rationale: The Clausius inequality states that for a cyclic process involving heat transfer at a single constant temperature, the integral of heat transfer divided by temperature (∫ dQ/T) must be less than or equal to zero. This inequality reflects the irreversibility of natural processes. Choice A is incorrect as there is a direct relationship between heat transfer and temperature in the Clausius inequality. Choice B is incorrect because the integral of dQ/T must be less than or equal to zero, not greater than or equal to zero. Choice C is incorrect because the integral of Q/T is not a constant in a cyclic process involving heat transfer at a single constant temperature.

Correct Answer: A

Rationale: The correct answer is A. Kinetic energy is proportional to the square of the velocity. When the speed drops from 60 mph to 30 mph, the kinetic energy is halved. Choice B is incorrect because halving the speed results in halving the kinetic energy, not doubling it. Choice C is incorrect because quadrupling the kinetic energy would require increasing the speed fourfold, not halving it. Choice D is incorrect because dividing the energy by four would imply a different relationship between speed and kinetic energy, which is not the case.

Correct Answer: C

Rationale: The formula to calculate the energy required to heat a substance is Q = m c ΔT, where m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. Given that 1 kilogram of water is equal to 1,000 grams, the mass (m) is 1,000 g, the specific heat capacity (c) of water is 4.2 J/g°C (not 2 J/g°C), and the change in temperature (ΔT) is 10°C. Substituting these values into the formula: Q = 1,000 4.2 10 = 42,000 J. Therefore, the correct energy required to heat 1 kilogram of water by 10°C is 42,000 J. Choices A, B, and D are incorrect as they do not consider the correct specific heat capacity of water or the conversion of mass to grams.

Correct Answer: A

Rationale: The correct answer is A: 'Its wavelength decreases.' The frequency and wavelength of a sound wave are inversely proportional. As the frequency of a sound wave increases (more oscillations per second), its wavelength decreases. This relationship is described by the formula: Speed of Sound = Frequency x Wavelength. Therefore, to maintain the speed of sound constant, when the frequency increases, the wavelength must decrease. Choices B, C, and D are incorrect because an increase in frequency does not lead to an increase in wavelength or changes in amplitude.

Correct Answer: D

Rationale: Surface tension creates a restoring force that holds the object on the surface. The liquid's surface behaves like a stretched membrane, and when disturbed, it tends to return the object to its original position, creating a restoring force. The other choices are incorrect: A buoyant force acts on objects submerged in a fluid, not floating on the surface; pressure differences usually affect sinking objects, not floating ones; drag force is a resistance force that opposes motion, not related to surface tension.

Correct Answer: A

Rationale: Density is calculated by dividing the mass of an object by its volume. In this case, the mass of the rock is 24 g and its volume is 6 cm3. By dividing 24 g by 6 cm3, we find that the density of the rock is 4 g/cm3. Choice A is the correct answer because density is expressed in units of mass per unit volume (g/cm3). Choice B is incorrect as it represents the reciprocal of density. Choices C and D are significantly higher values and do not match the calculated density of the rock.

Correct Answer: C

Rationale: The frequency of a wave is the number of cycles it completes in one second. A wave with a frequency of 60 hertz completes 60 cycles per second. Therefore, choice C is correct. Choice A is incorrect because a frequency of 60 hertz means 60 cycles per second, not per minute. Choice B is incorrect as the frequency of the wave does not determine the distance from crest to crest. Choice D is also incorrect as the frequency does not relate to the distance from crest to trough.

Correct Answer: A

Rationale: A refrigerator operates on a Carnot cycle by transferring heat from a cold reservoir to a hot reservoir. Choice A is correct because a refrigerator removes heat from a cold reservoir at a lower temperature. Choice B is incorrect as a refrigerator does not violate the first law of thermodynamics but rather requires work input to transfer heat. Choice C is incorrect as a refrigerator does not increase the total entropy of the universe. Choice D is incorrect because a refrigerator does not operate isothermally at both the hot and cold reservoirs.

Correct Answer: A

Rationale: In a parallel circuit, the current through each component is the same. This is because the components in a parallel circuit are connected across the same voltage source, so they all experience the same voltage across their terminals. The total current entering the parallel circuit is then split up among the various components, but the current through each component remains the same as the total current. Choices B, C, and D are incorrect. In a parallel circuit, voltage across each component may vary, resistance may differ, and wattage is related to power, not the equality of current through each component.