2023 - JAMB Physics Past Questions and Answers - page 5

The smallest temperature change that can be detected or measured.

The sensitivity of a thermometer refers to its ability to detect small changes in temperature. It is specifically defined as the smallest temperature change that can be detected or measured by the thermometer. Therefore, option D accurately describes the sensitivity of a thermometer.

- Object A experiences unstable equilibrium as it can move farther from its original position.
- Object B undergoes stable equilibrium as it can return to its original position.
- Object C undergoes neutral equilibrium as it can remain in a new position.

The correct option is: is equal to the number of free electrons

In an intrinsic semiconductor, the number of holes is equal to the number of free electrons. In an intrinsic semiconductor, electrons can break covalent bonds and create holes. The number of holes is essentially equal to the number of free electrons, maintaining overall charge neutrality in the material.

1. When a negatively charged rod is brought close to the metal sphere, it induces a separation of charges within the sphere. Electrons in the sphere are repelled by the negatively charged rod and move to the side of the sphere farthest from the rod, leaving the near side with a net positive charge.

2. If the sphere is then earthed (connected to the Earth), electrons will flow from the ground to the sphere, neutralizing the positive charge induced by the rod. After earthing, the sphere will have an excess of electrons and, thus, a net negative charge.

3. When the negatively charged rod is taken away, the sphere retains the excess electrons it gained during earthing, resulting in a net negative charge.

Therefore, the correct option is: The sphere will have a net negative charge.

\[ P_{\text{absolute}} = P_{\text{atmospheric}} + P_{\text{hydrostatic}} \]

where:
- \( P_{\text{atmospheric}} = 101.3 \, \text{kPa} \) (atmospheric pressure),
- \( P_{\text{hydrostatic}} = \rho \cdot g \cdot h \) (hydrostatic pressure).

Given:
- \( \rho = 1 \times 10^{-3} \, \text{kg/m}^3 \) (density of water),
- \( g = 9.8 \, \text{m/s}^2 \) (acceleration due to gravity),
- \( h = 32.8 \, \text{m} \) (depth of the lake).

Let's recalculate:

\[ P_{\text{hydrostatic}} = (1 \times 10^{-3} \, \text{kg/m}^3) \cdot (9.8 \, \text{m/s}^2) \cdot (32.8 \, \text{m}) \]

\[ P_{\text{hydrostatic}} = 0.0001 \, \text{kg/(m} \cdot \text{s}^2) \cdot 322.4 \, \text{m} \]

\[ P_{\text{hydrostatic}} = 32.24 \, \text{kPa} \]

Now, calculate \( P_{\text{absolute}} \):

\[ P_{\text{absolute}} = 101.3 \, \text{kPa} + 32.24 \, \text{kPa} \]

\[ P_{\text{absolute}} = 133.54 \, \text{kPa} \]

Therefore, the correct option is: 422.7 KPa

A pyrometer thermometer measures temperature from the thermal radiation emitted by objects. Pyrometers are specifically designed to measure high temperatures, and they operate based on the principle that the intensity and colour of the thermal radiation emitted by an object are related to its temperature. Pyrometers are commonly used in applications such as metalworking, industrial processes, and temperature measurement in furnaces.

Solution in Own Words:

To find the radius of an air bubble as it rises from a depth of 12 m below the water surface to the surface, we can use Boyle's law, which states that the product of pressure and volume is constant for a given mass of gas at constant temperature. 

Initially, the pressure (\(P_1\)) on the bubble at a depth of 12 m is the sum of atmospheric pressure and the pressure due to the water column above it, which is 22.34 m of water. The initial volume (\(V_1\)) is calculated using the formula for the volume of a sphere. 

As the bubble rises to the surface, the pressure (\(P_2\)) decreases to the atmospheric pressure of 10.34 m of water. The final volume (\(V_2\)) is again calculated using the volume formula. 

Applying Boyle's law (\(P_1V_1 = P_2V_2\)), we can set up an equation and solve for the final radius (\(r_2\)). 

\(r_1\) = 4.5cm, \( P_1\) = total pressure on the bubble at a depth of 12m from the surface.

\(P_1\) = 12 + 10.34 =22.34m

 \(V_1\) = \(\frac{4}{3}\)π× \(r^3_1\)

= \(\frac{4}{3}× π×{4.5^3cm^3}\)

\(P_2\) = 10.34m

\(V_2\)  = \(\frac{4}{3} {π}{r^3_2}\)

From Boyles Law,

\(P_1V_1\)  = \(P_2V_2\) 

22.34× \(\frac{4}{3}× π×{4.5^3}\) = 10.34 × \(\frac{4}{3}×π×{r^3_2}\)

22.34 × \(4.5^3\) = 10.34 × \(r^3_2\)

\(r^3_2\)= \(\^3√196.88\)

\(r^3_2\) = 5.82cm

To calculate the total heat required, we need to consider the following:

1. Heating the ice from \(-10^oC\) to \(0^oC\) using the specific heat capacity of ice.
2. Melting the ice at \(0^oC\) to water using the specific latent heat of fusion.
3. Heating the water from \(0^oC\) to \(10^oC\) using the specific heat capacity of water.

Let's calculate each part:

1. Heating ice from \(-10^oC\) to \(0^oC\):
   \[ Q_1 = mc\Delta T \]
   \[ Q_1 = 0.02 \, \text{kg} \times 2100 \, \text{J/kg} \, ^\circ\text{C} \times (0 - (-10)) \, ^\circ\text{C} \]
   \[ Q_1 = 0.02 \times 2100 \times 10 \]
   \[ Q_1 = 420 \, \text{J} \]

2. Melting the ice at \(0^oC\) to water:
   \[ Q_2 = mL_f \]
   \[ Q_2 = 0.02 \, \text{kg} \times 3.34 \times 10^5 \, \text{J/kg} \]
   \[ Q_2 = 6680 \, \text{J} \]

3. Heating water from \(0^oC\) to \(10^oC\):
   \[ Q_3 = mc\Delta T \]
   \[ Q_3 = 0.02 \, \text{kg} \times 4200 \, \text{J/kg} \, ^\circ\text{C} \times (10 - 0) \, ^\circ\text{C} \]
   \[ Q_3 = 0.02 \times 4200 \times 10 \]
   \[ Q_3 = 840 \, \text{J} \]

Now, add up the three quantities to get the total heat required:
\[ \text{Total heat} = Q_1 + Q_2 + Q_3 = 420 + 6680 + 840 = 7940 \, \text{J} \]

Therefore, the correct answer is: 7940 J

Nuclear fusion is the process responsible for the production of energy in stars, including our Sun. This process involves the fusion (combination) of light atomic nuclei to form a heavier nucleus, releasing a tremendous amount of energy in the process. In the core of stars like the Sun, hydrogen nuclei (protons) undergo nuclear fusion to form helium nuclei.

The basic fusion reaction occurring in stars, particularly in the Sun, is the proton-proton chain reaction. In this process, hydrogen nuclei fuse together to form helium, and the excess mass is converted into energy according to Einstein's mass-energy equivalence principle (E=mc²).

Nuclear reactions involve the release or absorption of energy through changes in atomic nuclei, and in the context of stars, nuclear fusion is the primary mechanism through which stars generate the energy that sustains their luminosity and heat. Therefore, Option C, "Nuclear fusion," is the correct choice for the process responsible for the production of energy in stars.

The beam balance works on the principle of moments. Moments are torques or turning forces that cause an object to rotate around a pivot or a fixed point. In a beam balance, the object to be weighed is placed on one side of a balanced beam, and standard weights are placed on the other side. When the beam is level, the moments on both sides are equal, indicating that the weights are in equilibrium. This principle is essential for accurate measurement of mass using a beam balance.