Heat and temperature. Convert to the Kelvin scale with T(K) = θ(°C) + 273; absolute zero, the temperature at which an ideal gas would exert zero pressure, is -273 °C (0 K). Heat gained or lost during a temperature change is Q = mcΔθ, with the specific heat capacity of water taken as 4200 J kg⁻¹ K⁻¹. During a change of state, temperature stays constant while latent heat Q = mL is absorbed or released: the specific latent heat of fusion of ice is 3.36 × 10⁵ J/kg and that of vaporisation of water is 2.26 × 10⁶ J/kg.
Gas laws and kinetic theory. Boyle's law: for a fixed mass of gas at constant temperature, pressure is inversely proportional to volume, so PV = constant (P₁V₁ = P₂V₂). Charles's law: at constant pressure, V/T = constant, with T in kelvin. Combined, they give the general gas equation P₁V₁/T₁ = P₂V₂/T₂; the ideal gas equation is PV = nRT. Kinetic theory explains gas pressure as molecular bombardment of the container walls.
Expansion and heat transfer. Linear expansivity α = ΔL/(L₀Δθ) is the increase in length per unit original length per unit rise in temperature; for a solid, cubic expansivity γ = 3α. Water is anomalous: it contracts when heated from 0 °C to 4 °C and has its maximum density at 4 °C. Heat travels by conduction (mainly in solids), convection (in liquids and gases, by movement of the fluid itself) and radiation, which needs no material medium.
Waves and sound. Key points for the UTME paper:
Light and optics. Snell's law: n = sin i / sin r = real depth / apparent depth, with n(glass) ≈ 1.5 and n(water) ≈ 1.33 (4/3). Total internal reflection happens only when light passes from a denser to a less dense medium with the angle of incidence greater than the critical angle C, where sin C = 1/n — the principle of optical fibres and the mirage. Mirrors and lenses obey 1/f = 1/u + 1/v with magnification m = v/u; a plane mirror forms a virtual, erect, laterally inverted image, the same size as the object and as far behind the mirror as the object is in front. Dispersion splits white light into its component colours, and all electromagnetic waves travel in a vacuum at c = 3.0 × 10⁸ m/s.
1. According to Boyle's law, for a fixed mass of gas at constant temperature, which of the following relationships is correct?
Boyle's law states that at constant temperature, PV = constant, so pressure and volume are inversely proportional for a fixed mass of gas. (JAMB UTME Physics Syllabus, Topic 14 (Gas Laws); Nelkon & Parker, Advanced Level Physics)
2. A fixed mass of gas occupies a volume of 400 cm3 at a pressure of 1.0 x 10^5 Pa. If the pressure is increased to 2.0 x 10^5 Pa at constant temperature, what is the new volume of the gas?
By Boyle's law, P1V1 = P2V2, so V2 = (1.0 x 10^5 x 400)/(2.0 x 10^5) = 200 cm3. (JAMB UTME Physics Syllabus, Topic 14 (Gas Laws))
3. Charles's law states that for a fixed mass of gas at constant pressure, the volume of the gas is directly proportional to its
Charles's law states that V/T = constant at constant pressure, meaning volume is directly proportional to the absolute temperature. (JAMB UTME Physics Syllabus, Topic 14 (Gas Laws); Nelkon & Parker, Advanced Level Physics)
4. A fixed mass of gas has a volume of 300 cm3 at 27°C. At constant pressure, what will its volume be when the temperature is raised to 127°C?
Converting to Kelvin, T1 = 300 K and T2 = 400 K; using V1/T1 = V2/T2 gives V2 = 300 x 400/300 = 400 cm3. (JAMB UTME Physics Syllabus, Topic 14 (Gas Laws); Topic 12 (Temperature and its Measurement))
5. Absolute zero, the temperature at which an ideal gas theoretically exerts zero pressure, corresponds to
Absolute zero is -273°C, which is 0 K on the Kelvin scale, using T(K) = θ(°C) + 273. (JAMB UTME Physics Syllabus, Topics 12 and 14 (Temperature and its Measurement; Gas Laws))
6. A gas occupies 2.0 x 10^-3 m3 at a pressure of 1.0 x 10^5 Pa and a temperature of 300 K. If the pressure changes to 1.5 x 10^5 Pa and the temperature to 450 K, what is the new volume of the gas?
Using P1V1/T1 = P2V2/T2, both pressure and temperature increase by the same factor of 1.5, so the volume remains unchanged at 2.0 x 10^-3 m3. (JAMB UTME Physics Syllabus, Topic 14 (Gas Laws))
7. Calculate the quantity of heat required to raise the temperature of 2 kg of water from 20°C to 40°C, given that the specific heat capacity of water is 4200 J kg^-1 K^-1.
Using Q = mcΔθ = 2 x 4200 x 20 = 1.68 x 10^5 J. (JAMB UTME Physics Syllabus, Topic 15 (Quantity of Heat); Okeke & Anyakoha, Senior Secondary School Physics)
8. How much heat is required to completely melt 2 kg of ice already at 0°C, given that the specific latent heat of fusion of ice is 3.36 x 10^5 J/kg?
Using Q = mL = 2 x 3.36 x 10^5 = 6.72 x 10^5 J; this heat changes the state of the ice without changing its temperature. (JAMB UTME Physics Syllabus, Topic 16 (Change of State); Nelkon & Parker, Advanced Level Physics)
9. Water shows anomalous expansion because it has its maximum density at
Water contracts when heated from 0°C to 4°C, so it has its maximum density at 4°C, unlike most substances which expand uniformly on heating. (JAMB UTME Physics Syllabus, Topic 13 (Thermal Expansion — anomalous expansion of water))
10. A metal has a linear expansivity of 2.0 x 10^-5 K^-1. What is the approximate cubic (volume) expansivity of the same metal?
Cubic expansivity is approximately three times the linear expansivity, so γ = 3α = 3 x 2.0 x 10^-5 = 6.0 x 10^-5 K^-1. (JAMB UTME Physics Syllabus, Topic 13 (Thermal Expansion))
11. The relationship between the speed (v), frequency (f) and wavelength (λ) of a wave is given by
The wave equation states that the speed of a wave equals the product of its frequency and wavelength, v = fλ. (JAMB UTME Physics Syllabus, Topic 20 (Waves — relationship between frequency, wavelength and velocity))
12. A wave has a frequency of 250 Hz and a wavelength of 1.2 m. Calculate the speed of the wave.
Using v = fλ = 250 x 1.2 = 300 m/s. (JAMB UTME Physics Syllabus, Topic 20 (Waves))
13. If a wave has a frequency of 50 Hz, what is its period?
The period is the reciprocal of frequency, T = 1/f = 1/50 = 0.02 s. (JAMB UTME Physics Syllabus, Topic 20 (Waves))
14. A man standing 170 m from a cliff claps his hands and hears the echo 1.0 s later. What is the speed of sound in air based on this observation?
For an echo, d = vt/2, so v = 2d/t = (2 x 170)/1.0 = 340 m/s, close to the typical speed of sound in air. (JAMB UTME Physics Syllabus, Topic 21 (Propagation of Sound Waves))
15. The normal range of audible frequencies for the human ear is
The normal human ear can detect sound frequencies from about 20 Hz to 20,000 Hz; frequencies above this are called ultrasonic. (JAMB UTME Physics Syllabus, Topic 22 (Characteristics of Sound Waves); Okeke & Anyakoha, Senior Secondary School Physics)
16. Polarisation can be observed in light waves but not in sound waves because
Only transverse waves can be polarised; since light is transverse and sound is longitudinal, only light can be polarised. (JAMB UTME Physics Syllabus, Topic 20 (Waves — properties: polarisation); Nelkon & Parker, Advanced Level Physics)
17. Sound waves cannot travel through a vacuum because sound is a
Sound is a longitudinal mechanical wave, so it needs particles of a medium to propagate and cannot travel through a vacuum. (JAMB UTME Physics Syllabus, Topic 21 (Propagation of Sound Waves))
18. A dog whistle emits sound at a frequency of 25,000 Hz. Why is this sound inaudible to a normal human but audible to a dog?
Since the normal human audible range is 20 Hz to 20,000 Hz, a 25,000 Hz sound is ultrasonic to humans but can still fall within a dog's wider hearing range. (JAMB UTME Physics Syllabus, Topic 22 (Characteristics of Sound Waves))
19. The speed of light in a vacuum, used for electromagnetic wave calculations in physics, is approximately
The speed of light in a vacuum is 3.0 x 10^8 m/s, the standard value used in electromagnetic wave calculations. (JAMB UTME Physics Syllabus, Topics 20 and 27 (Waves; Dispersion of Light — electromagnetic spectrum); Nelkon & Parker, Advanced Level Physics)
20. Which of the following sequences correctly lists electromagnetic waves in order of increasing wavelength (shortest to longest)?
In the electromagnetic spectrum, gamma rays have the shortest wavelength, followed by X-rays, ultraviolet, and then visible light with a longer wavelength. (JAMB UTME Physics Syllabus, Topic 27 (Dispersion of Light — electromagnetic spectrum); Nelkon & Parker, Advanced Level Physics)
21. A ray of light passes from air into glass with an angle of incidence of 30°. If the refractive index of the glass is 1.5, calculate the angle of refraction. (sin 30° = 0.5)
By Snell's law, n = sin i/sin r, so sin r = sin 30°/1.5 = 0.333, giving r = sin^-1(0.333) ≈ 19.5°. (JAMB UTME Physics Syllabus, Topic 25 (Refraction of Light — Snell's law))
22. A coin at the bottom of a pond appears to be at a depth of 90 cm when viewed vertically from above. If the refractive index of water is 4/3, calculate the real depth of the pond.
Since n = real depth/apparent depth, real depth = n x apparent depth = (4/3) x 90 = 120 cm. (JAMB UTME Physics Syllabus, Topic 25 (Refraction of Light — real and apparent depth))
23. Total internal reflection of a light ray can only occur when the light travels
Total internal reflection requires light to travel from an optically denser medium to a less dense one, with the angle of incidence exceeding the critical angle C, where sin C = 1/n. (JAMB UTME Physics Syllabus, Topic 25 (Refraction — critical angle and total internal reflection))
24. The principle of total internal reflection is applied in the working of
Optical fibres transmit light along their length using repeated total internal reflection at the core-cladding boundary. (JAMB UTME Physics Syllabus, Topic 25 (Refraction — critical angle and total internal reflection))
25. An object is placed 15 cm in front of a converging (convex) lens of focal length 10 cm. Calculate the image distance from the lens.
Using 1/f = 1/u + 1/v: 1/10 = 1/15 + 1/v, giving 1/v = 1/30, so v = 30 cm. (JAMB UTME Physics Syllabus, Topic 25 (Refraction — lens formula))
26. According to Boyle's law, for a fixed mass of gas at constant temperature, the pressure of the gas is __ its volume.
Boyle's law states that PV = constant at constant temperature, meaning pressure is inversely proportional to volume. (JAMB UTME Physics Syllabus, Topic 14 (Gas Laws); Nelkon & Parker, Advanced Level Physics)
27. What is the value of absolute zero on the Celsius temperature scale?
Absolute zero, the temperature at which an ideal gas would exert zero pressure, is -273 °C, equivalent to 0 K. (JAMB UTME Physics Syllabus, Topics 12 and 14 (Temperature and its Measurement; Gas Laws))
28. Which equation correctly represents Boyle's law for a fixed mass of gas at constant temperature?
Boyle's law states that PV = constant, so P1V1 = P2V2 for the same gas at constant temperature. (JAMB UTME Physics Syllabus, Topic 14 (Gas Laws))
29. Charles's law states that for a fixed mass of gas at constant pressure, the volume of the gas is __ its absolute temperature.
Charles's law states that V/T = constant at constant pressure, i.e., volume is directly proportional to the absolute (Kelvin) temperature. (JAMB UTME Physics Syllabus, Topic 14 (Gas Laws); Nelkon & Parker, Advanced Level Physics)
30. What is the equivalent of 0 °C on the Kelvin scale?
Using T(K) = θ(°C) + 273, 0 °C converts to 273 K. (JAMB UTME Physics Syllabus, Topics 12 and 14 (Temperature and its Measurement; Gas Laws))
31. A fixed mass of gas occupies a volume of 6.0 m^3 at a pressure of 2.0 x 10^5 Pa. If the gas is compressed at constant temperature to a volume of 4.0 m^3, what is the new pressure?
By Boyle's law, P1V1 = P2V2, so P2 = (2.0 x 10^5 x 6.0)/4.0 = 3.0 x 10^5 Pa. (JAMB UTME Physics Syllabus, Topic 14 (Gas Laws))
32. A gas has a volume of 300 cm^3 at 27 °C. At constant pressure, what will be its volume at 127 °C?
Using Charles's law V1/T1 = V2/T2 with temperatures in Kelvin (300 K and 400 K), V2 = 300 x (400/300) = 400 cm^3. (JAMB UTME Physics Syllabus, Topic 14 (Gas Laws); Nelkon & Parker, Advanced Level Physics)
33. The general gas equation P1V1/T1 = P2V2/T2 is obtained by combining which two gas laws?
The general gas equation combines Boyle's law (PV = constant at constant T) and Charles's law (V/T = constant at constant P). (JAMB UTME Physics Syllabus, Topic 14 (Gas Laws))
34. In the ideal gas equation PV = nRT, what does the letter n represent?
In PV = nRT, n represents the number of moles of the gas, R is the molar gas constant, and T is the absolute temperature. (JAMB UTME Physics Syllabus, Topic 14 (Gas Laws))
35. According to the kinetic theory of matter, the absolute temperature of a gas is a measure of...
Kinetic theory relates the absolute temperature of a gas directly to the average kinetic energy of its molecules; this underlies the gas laws. (JAMB UTME Physics Syllabus, Topic 14 (Gas Laws — Kinetic Theory); Okeke & Anyakoha, Senior Secondary School Physics)