Nokea
Which of the following materials has the lowest density?
- A. Water
- B. Cork
- C. Aluminum
- D. Steel
Correct Answer: B
Rationale: Cork has the lowest density among the given options. Cork is a lightweight material derived from the bark of cork oak trees and is known for its low density, making it float on water. Water, aluminum, and steel have higher densities compared to cork. Water is denser than cork because it has a consistent density of 1 g/cm³. Aluminum and steel are metals with much higher densities due to their atomic structures, making them denser than cork.
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When a gas is compressed isothermally, we can say that:
- A. The gas performs work on the surroundings, and its internal energy increases.
- B. The gas performs work on the surroundings, and its internal energy decreases.
- C. The surroundings perform work on the gas, and its internal energy increases.
- D. The surroundings perform work on the gas, and its internal energy decreases.
Correct Answer: D
Rationale: When a gas is compressed isothermally, the surroundings perform work on the gas. In this process, since the temperature remains constant (isothermal), the internal energy of the gas does not change. Therefore, the correct answer is that the surroundings perform work on the gas, and its internal energy decreases. Choices A, B, and C are incorrect because they incorrectly describe the direction of work and the change in internal energy during an isothermal compression.
The efficiency (η) of a heat engine is defined as the ratio of the net work done (Wnet) by the engine to the heat input (Qh) from the hot reservoir. The relationship is expressed as:
- A. η = Wnet / Qh
- B. η = Qh / Wnet
- C. η = Wnet x Qh
- D. η = (Wnet + Qh) / 2
Correct Answer: A
Rationale: The correct formula for efficiency (η) of a heat engine is η = Wnet / Qh. Efficiency is defined as the ratio of the net work done by the engine (Wnet) to the heat input from the hot reservoir (Qh). This formula shows how effectively the engine converts heat into useful work, making choice A the correct answer. Choices B, C, and D present incorrect relationships between efficiency, net work done, and heat input, leading to their incorrectness.
The Prandtl number (Pr) is a dimensionless property relating:
- A. Viscosity and thermal diffusivity
- B. Density and pressure
- C. Surface tension and pressure
- D. Reynolds number and flow regime
Correct Answer: A
Rationale: The Prandtl number (Pr) is a dimensionless number used to characterize fluid flow. It is the ratio of momentum diffusivity to thermal diffusivity. In simpler terms, it relates the ability of a fluid to conduct heat to its ability to conduct momentum. Therefore, the correct relationship is between viscosity and thermal diffusivity, making choice A the correct answer. Choices B, C, and D are incorrect because they do not represent the properties that the Prandtl number relates.
Fluids can be categorized based on their shear stress-strain rate relationship. An ideal fluid exhibits:
- A. Zero shear stress at any strain rate
- B. Linear relationship between shear stress and strain rate (Newtonian)
- C. Non-linear relationship between shear stress and strain rate (Non-Newtonian)
- D. High dependence of viscosity on temperature
Correct Answer: A
Rationale: An ideal fluid, often referred to as an inviscid fluid, is a theoretical concept used in fluid mechanics to simplify calculations. It is characterized by having zero shear stress at any strain rate. In reality, such fluids do not exist, but they serve as a useful starting point for understanding fluid behavior in idealized situations. Choice B is incorrect because a linear relationship between shear stress and strain rate defines a Newtonian fluid, not an ideal fluid. Choice C is incorrect because a non-linear relationship between shear stress and strain rate characterizes Non-Newtonian fluids, not ideal fluids. Choice D is incorrect because the high dependence of viscosity on temperature is a characteristic seen in real fluids and does not define an ideal fluid.
Household alternating current typically has a frequency of 60 Hz. Which statement is true?
- A. The circuit is suitable for lighting 60-watt bulbs.
- B. Circuits in the home may carry a current of 60 amperes.
- C. The expected voltage drop is 60 volts per meter.
- D. Electrons complete a cycle 60 times per second.
Correct Answer: D
Rationale: The correct answer is D. Electrons complete a cycle 60 times per second when the frequency of the current is 60 Hz. This frequency indicates that the current changes direction 60 times per second, causing the electrons to complete a full cycle back and forth through the circuit at the same rate. Choice A is incorrect because the power rating of a bulb (in watts) is not directly related to the frequency of the current. Choice B is incorrect as typical household circuits do not carry currents as high as 60 amperes. Choice C is incorrect as the expected voltage drop is not measured in volts per meter for household alternating current circuits.