The Mass of Air Rises: How and Why

Question 1 

As a mass of air rises, it expands leading to the increase of its volume. The expansion of the air as it rises leads to the reduction of its temperature. 

Question 2 

The tension in the string is as a result of centrifugal force. 

F = mv²/r Where m = mass, v = velocity, r = radius 

F = = 7.2 N 

Tension = 7.2 N 

Question 3 

Torque = Lever arm distance × Force 

Torque = 0.2 m × 50 N = 10 Nm 

Question 4 

The direction of coastal winds changes from day to night due to differences in the levels of heating of the land mass and ocean during the day and night. Water has higher specific heat than the land mass. During the day, the land mass gets heated more than the ocean making the air near the land mass to be lighter and warmer. Consequently, cooler air from the ocean flows to the land mass. On the other hand, during the night the ocean cools more slowly than the land, thus the cooler air from the land flows towards the ocean. 

Question 5 

Terrestrial radiation is the longwave electromagnetic radiation emitted by the earth’s surface and the atmosphere. This radiation is produced by earth materials that are naturally radioactive such as radon and uranium. 

Question 6 

Amount of energy = Q = mL 

Where m = mass 

L is the latent heat of vaporization of water = 540 cal/g/°C 

Amount of energy = 1g × 540 cal/g/°C = 540 Calories 

Q = 540 Calories 

Question 7 

Sublimation is the transfer of a substance from the solid state to the gas state without going through the liquid state. 

Question 8 

0.5 EP = Q (mc ΔT) 

Potential energy = mgh 

0.5 mgh = mc ΔT 

The mass on both sides of the equation cancel out to give: 

0.5 gh = c ΔT 

g = 9.8 m/s² while c = 450J/kgC 

0.5 × 9.8 m/s² × 100 m = 450J/kgC × ΔT 

ΔT = (0.5 × 9.8 m/s² × 100 m) / 450J/kgC = 1.1 °C 

The temperature increase = 1.1 °C 

Question 9 

The third law of thermodynamics states that the entropy of a system will approach a constant value as the temperature approaches zero. According to the law, the entropy of a perfect crystal at the absolute zero temperature will exactly be equal to zero. 

Question 10 

Carnot’s engine efficiency formula is used 

Efficiency = 1 -  where T c and T h are the cold and hot reservoir temperatures in Kelvin 

T c = 320 + 273 = 593 K 

T h = 600 + 273 = 873 K 

Efficiency = 1 -  = 0.32 

Efficiency = 0.32 × 100% = 32% 

Question 11 

101.7 MHz = 101.7 million hertz (Hz) 

Hertz represents the vibrations per second 

Thus, 101.7 MHz represents 101.7 million vibrations per second = 101,700,000 vibrations per second 

Question 12 

The superimposition principle states that when waves overlap, they form a single wave whose resultant disturbance is obtained by summing up the disturbances of the individual waves. 

Question 13 

In the Doppler effect, the frequency changes while the wave speed remains constant. 

Question 14 

Speed of a wave = wave frequency × wavelength 

Speed = 2 Hz × 1.5 m = 3.0 m/s 

Question 15 

The period, T is calculated as T = (1 swing × 75 seconds) / 15 swings = 5 s 

T = 2 π √ 

5 s = 2 π √ 

Square each component to get 

5² = 4 π² 

g =  = 1.579 ≈ 1.6 m/s² 

Question 16 

The average hearing range of a young person is from 20 Hz to 20,000 Hz 

Question 17 

A wave may cancel the other when two identical waves arrive exactly out of phase, that is, with the crest aligned to the trough. The resulting superposition is termed as destructive interference and the resultant amplitude is zero, hence the cancelling of the waves. 

Question 18 

Fourier came to the discovery that complex periodic wave patterns may be broken down into simple sine waves that add together.