2024 - JAMB Physics Past Questions and Answers - page 9

Here's how to solve the problem using Gay-Lussac's Law (pressure-temperature relationship) for a constant volume:

1. Identify the Knowns:
   • Initial pressure, P₁ = 40 mmHg
   • Initial temperature, T₁ = 298 K
   • Final temperature, T₂ = 348 K
2. Identify the Unknown:
   • Final pressure, P₂ = ?
3. Apply Gay-Lussac's Law:
   • The formula is: P₁/T₁ = P₂/T₂
4. Solve for P₂:
   • P₂ = (P₁ * T₂) / T₁
   • P₂ = (40 mmHg * 348 K) / 298 K
   • P₂ ≈ 46.71 mmHg

Here's how to solve the problem:

1. Calculate the heat energy generated by the resistor:
   • The power (P) dissipated by a resistor is given by P = I²R, where I is the current and R is the resistance.
   • P = (10 A)² * 2 Ω = 200 W
   • The heat energy (Q) generated in 20 seconds is Q = P * t, where t is time.
   • Q = 200 W * 20 s = 4000 J
2. Calculate the specific latent heat of vaporization (L):
   • The heat energy (Q) used to evaporate the liquid is given by Q = mL, where m is the mass of the liquid and L is the specific latent heat of vaporization.
   • L = Q / m
   • L = 4000 J / (5 x 10^-3 kg) = 8.0 x 10⁵ J/kg

To find the horizontal component of the force, we use the cosine function since the angle is with respect to the horizontal.

1. Identify the given:
   • Force (F) = 150 N
   • Angle (θ) = 60°
2. Formula:
   • Horizontal component (Fx) = F * cos(θ)
3. Calculation:
   • Fx = 150 N * cos(60°)
   • Fx = 150 N * 0.5
   • Fx = 75 N

Therefore, the horizontal component of the applied force is 75 N.

The formula to convert Celsius to Fahrenheit is:

F = (9/5)C + 32

Where F is the temperature in Fahrenheit and C is the temperature in Celsius.

Substitute C = 60:

F = (9/5) * 60 + 32

F = 108 + 32

F = 140

Therefore, 60°C is equal to 140°F.

The emergent velocity of an ion moving through combined electric and magnetic fields can be understood by considering the forces acting on the ion:

• Electric Force: The electric force on a charge q in an electric field E is given by F_E = qE. This force causes the ion to accelerate in the direction of the electric field (for a positive charge) or opposite to the electric field (for a negative charge).
• Magnetic Force: The magnetic force on a charge q moving with velocity v in a magnetic field B is given by F_B = qvB sinθ, where θ is the angle between the velocity and the magnetic field. If the electric and magnetic forces are balanced, the ion will move with a constant velocity.

For the ion to pass through the fields undeflected, the electric force and magnetic force must balance each other. Assuming the electric and magnetic fields are perpendicular to each other and to the velocity of the ion, we have:

Dividing both sides by qB:

Therefore, the emergent velocity of the ion is E/B.

According to the kinetic theory of gases, the pressure exerted by a gas on the walls of its container arises from the collisions of the gas molecules with the walls. Here's why option B is the most appropriate:

• B. rate of change of momentum imparted by the walls per second per unit area: This statement accurately reflects the kinetic theory. Pressure is defined as force per unit area. The force exerted by the gas molecules on the walls is due to the change in momentum of the molecules during collisions. The rate of this momentum change over a given area determines the pressure.

The land and sea breeze is primarily caused by convection.

• Convection: This is the process of heat transfer through the movement of fluids (in this case, air). The land heats up and cools down more quickly than the sea.
• Land Breeze: At night, the land cools faster, causing the air above it to cool and become denser. This denser air sinks, creating a high-pressure zone over the land. Meanwhile, the sea, which is warmer, causes the air above it to rise. This creates a low-pressure zone over the sea, and the air flows from the land (high pressure) to the sea (low pressure).
• Sea Breeze: During the day, the land heats up faster, causing the air above it to heat and rise. This creates a low-pressure zone over the land. The air over the cooler sea is denser, creating a high-pressure zone. The air then flows from the sea (high pressure) to the land (low pressure).

Conduction and radiation also play a role in heat transfer, but they are not the primary drivers of the land and sea breeze.