A closed cubical icebox has side 1/2 m. Treat each of its six outer walls as a flat slab, with area equal to the square of the side and thickness 0.05 m. The conductivity is 0.01 W m^-1 K^-1. The outside temperature is 40°C, and the ice-water mixture inside stays at 0°C. At the start there is 5 kg of ice. Ignoring the edges, how much ice is left after 4 h? Use L_f = 335000 J/kg. Give an exact expression in kg.
(a)(5 + 172800/335000) kg
(b)(5 − 28800/335000) kg
(c)(5 − 172800/335000) kg
Show answer
(c) (5 − 172800/335000) kg
Use total exposed area 6a² in H=kAΔT/L. The conducted energy Ht melts mass Ht/Lf; subtract this from the initial ice mass.
Question 2
A closed cubical icebox has six flat walls. Each wall has area (1/2 m)² and thickness 0.05 m. The conductivity is 0.01 W m^-1 K^-1. The outside temperature is 40°C, and the ice inside stays at 0°C as it melts. How long does it take to melt 9/25 kg of ice? Use L_f = 300000 J/kg, and ignore the edges.
(a)150 min
(b)900 min
(c)25 min
Show answer
(a) 150 min
All six faces conduct in parallel, giving H=6ka²ΔT/L. Set Ht=mLf and convert seconds to minutes.
Thermometric scales and gas thermometers
Question 3
A fixed amount of ideal gas in a rigid container has pressure 100 kPa at 27°C. What pressure does it have at 327°C? Use T(K) = t(°C) + 273.
(a)200 kPa
(b)10900/9 kPa
(c)50 kPa
Show answer
(a) 200 kPa
At fixed amount and volume, pressure is proportional to absolute temperature. Convert both temperatures to kelvin before forming the ratio.
Blackbody spectra and thermal-radiation laws
Question 4
The graph shows schematic spectra of blackbodies A and B. Only the horizontal wavelength positions are to scale; the curve heights are schematic. Using the peak wavelengths and Wien’s law, what is the ratio T_A : T_B?
(a)1 : 1
(b)1 : 2
(c)2 : 1
Show answer
(b) 1 : 2
Wien’s law gives λ_max T = constant. The temperature ratio is the inverse of the peak-wavelength ratio.
Question 5
A radiator’s emissivity and area remain fixed. What is emitted power at 327°C divided by emitted power at 27°C? Use T(K)=t(°C)+273 and ignore absorbed power.
(a)16
(b)(327/27)^4
(c)2
Show answer
(a) 16
Stefan–Boltzmann emitted power is proportional to absolute temperature to the fourth power. Convert both readings to kelvin before taking their ratio.
Free expansion and constrained thermal stress
Question 6
A straight rod is rigidly clamped at both ends and heated uniformly by 20 K. Its length cannot change. Y = 100 GPa and α = 20 × 10^-6 K^-1. What thermal stress develops in the elastic regime?
(a)40 MPa, compressive
(b)0 MPa because its length is unchanged.
(c)40 MPa, tensile
Show answer
(a) 40 MPa, compressive
The supports prevent positive free thermal strain αΔT. The compensating elastic strain is compressive, with stress magnitude YαΔT.
Linear, area and volume expansion
Question 7
A free sheet has a circular hole of diameter 40 mm. It is heated uniformly by 100 K; linear expansion coefficient α = 17 × 10^-6 K^-1. What is the signed change in hole diameter, neglecting higher-order effects?
(a)-17/250 mm
(b)17/250 mm
(c)0 mm
Show answer
(b) 17/250 mm
Imagine the hole filled with the same material during uniform expansion. Its diameter expands by αDΔT, so the change is positive.
Thermal density change and anomalous water
Question 8
A sealed fixed mass of liquid expands to 101/100 times its original volume. What is final density/original density?
(a)1
(b)101/100
(c)100/101
Show answer
(c) 100/101
Density is mass divided by volume. At conserved mass the density ratio is the reciprocal of the volume ratio.
Heat capacities, power and calorimetry
Question 9
A hot metal sample of mass 1/5 kg at 100°C is placed in water and a calorimeter initially at 20°C. Their heat capacities are 400 J/K and 100 J/K respectively. The insulated system reaches 30°C, with no phase change. What is the metal’s specific heat capacity?
(a)2000/7 J kg^-1 K^-1
(b)2500/7 J kg^-1 K^-1
(c)17500 J kg^-1 K^-1
Show answer
(b) 2500/7 J kg^-1 K^-1
Hot metal loses mc(Th−Tf). Water and vessel together gain (C_water+C_vessel)(Tf−Tc); equate these to solve c.
Phase-change energy and heating curves
Question 10
A pure substance is heated at constant pressure as shown. How much heat is absorbed during the horizontal phase-change segment?
(a)0 kJ because temperature is constant.
(b)50 kJ
(c)30 kJ
Show answer
(c) 30 kJ
The horizontal axis measures cumulative supplied heat. Subtract the heat coordinates at the two ends of the plateau; zero temperature change does not mean zero heat.
Question 11
At 1 atm, 1 kg of ice initially at −10°C becomes steam at 100°C. Use c_ice = 2 kJ kg^-1 K^-1, c_water = 4 kJ kg^-1 K^-1, L_f = 330 kJ/kg and L_v = 2260 kJ/kg. Ignore the container. What total heat is required?
(a)420 kJ
(b)3010 kJ
(c)2590 kJ
Show answer
(b) 3010 kJ
Warm the ice to 0°C, melt it, warm the liquid to 100°C and then vaporise it. Add all four positive energy contributions.
Pressure, phase coexistence and triple points
Question 12
Pure water in a sealed industrial boiler is held at 3 atm. Compared with its normal boiling point at 1 atm, how does its boiling temperature change?
(a)It stays exactly 100°C because boiling point is independent of pressure.
(b)It is lower than 100°C.
(c)It is higher than 100°C.
Show answer
(c) It is higher than 100°C.
The normal boiling point refers to 1 atm. Increasing ambient pressure raises water’s equilibrium boiling temperature.
Temperature, heat and energy transfer
Question 13
A small metal ball at 80°C is put in thermal contact with a water bath of 10 times its mass at 20°C. Initially, which direction does heat flow?
(a)From the ball to the bath.
(b)From the bath to the ball because the bath is larger.
(c)No heat flows until their total energies become equal.
Show answer
(a) From the ball to the bath.
Compare temperatures to determine spontaneous heat-flow direction. The smaller ball is hotter, so it initially transfers heat to the bath.
Convection, radiation and thermal insulation
Question 14
A region of air is heated from below in gravity and undergoes ordinary thermal expansion. Why can that region rise in natural convection?
(a)All fluid rises at once, regardless of temperature differences.
(b)Its density increases, so the denser hot region floats upward.
(c)Its density decreases, so surrounding denser fluid supplies an upward buoyant effect.
Show answer
(c) Its density decreases, so surrounding denser fluid supplies an upward buoyant effect.
Heating expands this fluid and lowers its density. Density contrast in gravity drives the buoyant circulation.
Newton cooling and excess temperature
Question 15
In constant surroundings at 20°C, a body obeying Newton cooling cools from 60°C to 40°C in 5 min. What is its temperature after one more equal interval?
(a)100°C
(b)20°C
(c)30°C
Show answer
(c) 30°C
The first interval halves the temperature excess above ambient. The next equal interval halves the remaining excess, rather than repeating the previous absolute drop.
Common misconception in Thermal Properties of Matter
Can a temperature rise be used as the only measure of energy added?
Wrong
If ice stays at 0 °C while melting, it absorbs no energy.
Why it feels right. The temperature reading stays fixed.
Right
Energy can change the state at constant temperature.
Worked example
The flat part is the melting interval. Heat is added while the mixture stays near 0 °C.
Heat a mixture of ice and water near 0 °C at atmospheric pressure.
The ice melts before the mixture’s temperature rises.
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