Which of the following statements is true about a refrigerator?
- A. It operates on a Carnot cycle and removes heat from a cold reservoir at a lower temperature.
- B. It violates the first law of thermodynamics by creating cold.
- C. It increases the total entropy of the universe.
- D. It operates isothermally at both the hot and cold reservoirs.
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.
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A rock has a volume of 6 cm3 and a mass of 24 g. What is its density?
- A. 4 g/cm3
- B. 4 cm3/g
- C. 144 g/cm3
- D. 144 cm3/g
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.
For steady, incompressible flow through a pipe, the mass flow rate (á¹) is related to the fluid density (Ï), cross-sectional area (A), and average velocity (v) via the continuity equation:
- A. á¹ cannot be determined without additional information
- B. á¹ = ÏvA
- C. Bernoulli's principle is solely applicable here
- D. The equation of state for the specific fluid is required
Correct Answer: B
Rationale: The continuity equation for steady, incompressible flow states that the mass flow rate is the product of the fluid's density, velocity, and cross-sectional area. Hence, á¹ = ÏvA. Choice A is incorrect because the mass flow rate can be determined using the given formula. Choice C is incorrect as Bernoulli's principle does not directly relate to the mass flow rate calculation. Choice D is incorrect as the equation of state is not needed to calculate the mass flow rate in this scenario.
A 120-volt heat lamp draws 25 amps of current. What is the lamp's resistance?
- A. 96 ohms
- B. 104 ohms
- C. 150 ohms
- D. 4.8 ohms
Correct Answer: D
Rationale: To find the resistance of the lamp, we use Ohm's Law, which states that resistance (R) is equal to voltage (V) divided by current (I), expressed as: R = V / I. Given that the voltage (V) is 120 volts and the current (I) is 25 amps, we substitute these values into the formula: R = 120 V / 25 A = 4.8 ohms. Therefore, the resistance of the lamp is 4.8 ohms. Choice A, 96 ohms, is incorrect as it is not the result of the correct calculation. Choice B, 104 ohms, is incorrect as it does not match the calculated resistance. Choice C, 150 ohms, is incorrect as it is not the correct resistance value obtained through the calculation.
Entropy (S) is a thermodynamic property related to the system's disorder. According to the second law of thermodynamics, in a spontaneous process:
- A. The total entropy of the system and surroundings increases.
- B. The total entropy of the system and surroundings decreases.
- C. The total entropy of the system remains constant.
- D. The total entropy of the surroundings increases, while the system's entropy decreases.
Correct Answer: A
Rationale: The second law of thermodynamics asserts that the entropy of an isolated system (or the combined system and surroundings) will always increase in a spontaneous process, reflecting an increase in disorder. Therefore, the correct answer is that the total entropy of the system and surroundings increases. Choice B is incorrect because entropy always tends to increase in a spontaneous process, as dictated by the second law of thermodynamics. Choice C is incorrect as entropy typically increases in natural processes. Choice D is incorrect because the second law of thermodynamics states that the total entropy of the system and surroundings always increases in a spontaneous process.
The speed of sound in dry air at 20°C is 343 m/s. If the wavelength of a sound wave is 5 m, what is its frequency?
- A. 171.5 Hz
- B. 79 Hz
- C. 68.6 Hz
- D. 63.6 Hz
Correct Answer: C
Rationale: The speed of sound (v) can be calculated using the formula: v = f λ, where f is the frequency and λ is the wavelength. Given that the speed of sound is 343 m/s and the wavelength is 5 m, we can rearrange the formula to solve for frequency: f = v / λ = 343 / 5 = 68.6 Hz. Therefore, the correct frequency is 68.6 Hz. Choices A, B, and D are incorrect as they do not result from the correct calculation based on the given values.
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