Physics 2014 Jamb Examination

Nuclear energy involves the release of massive amounts of heat through processes like nuclear fission. In a nuclear power plant, this heat is used to boil water into steam. The high-pressure steam then turns a turbine (mechanical energy), which is connected to a generator that converts the rotational energy into electrical energy. Therefore, the ultimate purpose of harnessing nuclear heat in this context is the generation of electricity.

Efficiency (\(\eta\)) is defined as the ratio of Mechanical Advantage (MA) to Velocity Ratio (VR), expressed as a percentage:\[ \eta = \frac{MA}{VR} \times 100 \]Given:
\(\eta = 75\%\)
\(VR = 4\)
\(\text{Load} = 1000\text{N}\)
First, find the MA:\[ 75 = \frac{MA}{4} \times 100 \]\[ 0.75 = \frac{MA}{4} \]\[ MA = 0.75 \times 4 = 3 \]Since \(MA = \frac{\text{Load}}{\text{Effort}}\):\[ 3 = \frac{1000}{\text{Effort}} \]\[ \text{Effort} = \frac{1000}{3} = 333.33\text{N} \]

To find the efficiency, we need the Mechanical Advantage (MA) and the Velocity Ratio (VR).
\(MA = \frac{\text{Load}}{\text{Effort}} = \frac{800}{250} = 3.2\)
For a wheel and axle, \(VR = \frac{\text{Radius of Wheel (R)}}{\text{Radius of Axle (r)}}\):\[ VR = \frac{800}{200} = 4 \]Efficiency (\(\eta\)) is:\[ \eta = \frac{MA}{VR} \times 100 \]\[ \eta = \frac{3.2}{4} \times 100 = 0.8 \times 100 = 80\% \]

Tensile stress is defined as the force applied per unit cross-sectional area.\[ \text{Stress} = \frac{\text{Force (F)}}{\text{Area (A)}} \]Given:
\(F = 500\text{N}\)
\(A = 0.2\text{m}^2\)\[ \text{Stress} = \frac{500}{0.2} \]\[ \text{Stress} = 2500\text{Nm}^{-2} \]In scientific notation, this is \(2.5 \times 10^3\text{Nm}^{-2}\).

During the night, the Earth's surface loses heat through radiation, causing the temperature of the grass and other objects to drop. If the temperature falls below the dew point of the surrounding air, the water vapour in the air condenses directly onto these cool surfaces. These resulting water droplets are known as dew. Fog and mist involve water droplets suspended in the air, while hail is a form of solid precipitation.

The relationship between the Kelvin scale and the Celsius scale is given by the formula:\[ T(K) = \theta(^{\circ}\text{C}) + 273.15 \]To find the Celsius equivalent of 20K:\[ \theta = 20 - 273 \]\[ \theta = -253^{\circ}\text{C} \]

Charles's Law states that for a fixed mass of gas at constant pressure, the volume (\(V\)) is directly proportional to its absolute temperature (\(T\)). Mathematical representation:\[ V \propto T \implies \frac{V}{T} = \text{constant} \]This can be written as \(V^1 T^{-1} = \text{constant}\). To match the general equation \(P^a V^b T^c = \text{constant}\), the pressure term (P) must be absent (meaning its exponent \(a = 0\)), the exponent of volume \(b\) must be 1, and the exponent of temperature \(c\) must be -1. Thus, \(a=0, b=1, c=-1\).

Heat capacity (or thermal capacity) is defined as the amount of heat energy required to raise the temperature of an entire object or body by one unit of temperature (1 Kelvin or 1 degree Celsius). This differs from 'Specific' heat capacity, which refers to the heat required per unit mass (e.g., for 1kg of the substance). Since the question refers to the 'body' as a whole rather than a unit mass, the correct term is heat capacity.

The melting point is the temperature at which a substance changes from a solid to a liquid. For a pure substance under constant pressure, this temperature is the same as the temperature at which the liquid changes back into a solid, which is known as the solidification (or freezing) temperature. At this specific temperature, the solid and liquid phases exist in equilibrium.

Air can hold a certain amount of water vapour depending on its temperature; warmer air can hold more. If a volume of air is cooled, it eventually reaches a temperature where the amount of water vapour it contains is the maximum it can possibly hold (saturation). This critical temperature is called the dew point. If the air is cooled any further, condensation will occur.