Edexcel A-Level Physics: Thermodynamics

A solid block of pure ice at $-10\ \text{°C}$−10 °C is heated at a steady rate by an electrical heater until it has been completely converted into water vapour. A datalogger records the temperature of the sample throughout, producing a heating curve with two horizontal sections (plateaux) separated by sloping sections.

Explain, in terms of the kinetic and potential energies of the molecules, why the temperature rises during the sloping sections but stays constant during the two plateaux, even though energy is supplied to the sample at a constant rate throughout.

(6 marks)

A laboratory heater is used to convert a $0.25\ \text{kg}$0.25 kg block of ice, initially at $0\ \text{°C}$0 °C, completely into steam at $100\ \text{°C}$100 °C. The process happens in three stages: the ice melts to water at $0\ \text{°C}$0 °C, the water is then warmed to $100\ \text{°C}$100 °C, and finally the water is boiled away to steam at $100\ \text{°C}$100 °C. Assume no energy is lost to the surroundings.

Quantity	Value
Mass of sample, $m$m	0.25 kg
Specific latent heat of fusion of ice, $L_f$Lf​	$3.34 \times 10^{5}\ \text{J kg}^{-1}$3.34×105 J kg−1
Specific heat capacity of water, $c$c	$4200\ \text{J kg}^{-1}\ \text{K}^{-1}$4200 J kg−1 K−1
Specific latent heat of vaporisation of water, $L_v$Lv​	$2.26 \times 10^{6}\ \text{J kg}^{-1}$2.26×106 J kg−1

(a) Calculate the energy needed to melt the ice into water at $0\ \text{°C}$0 °C. (2 marks)

(b) Calculate the energy needed to warm that water from $0\ \text{°C}$0 °C to $100\ \text{°C}$100 °C. (2 marks)

(c) Calculate the energy needed to boil the water into steam at $100\ \text{°C}$100 °C, and hence state the total energy supplied across all three stages. (2 marks)

A fixed mass of gas is slowly compressed in a sealed syringe held in a water bath at a constant temperature. For each setting, the pressure $p$p and the volume $V$V of the trapped gas are recorded. One volume reading was not taken.

Pressure $p$p / kPa	100	120	150	200	240
Volume $V$V / cm³	24.0	20.0	16.0	—	10.0

(a) By calculating a suitable quantity for the four complete readings, show that the data are consistent with Boyle's law, and state the two conditions Boyle's law requires. (3 marks)

(b) Use Boyle's law to determine the missing volume at a pressure of $200\ \text{kPa}$200 kPa. (2 marks)

A scuba diver's air cylinder has an internal volume of $12\ \text{L}$12 L and is filled with compressed air to a pressure of $1.8 \times 10^{7}\ \text{Pa}$1.8×107 Pa at a temperature of $17\ \text{°C}$17 °C. The compressed air may be treated as an ideal gas.

Take the molar gas constant $R = 8.31\ \text{J mol}^{-1}\ \text{K}^{-1}$R=8.31 J mol−1 K−1 and the Avogadro constant $N_A = 6.02 \times 10^{23}\ \text{mol}^{-1}$NA​=6.02×1023 mol−1.

(a) Calculate the amount of gas (in moles) inside the cylinder. (3 marks)

(b) Hence calculate the number of gas molecules inside the cylinder. (2 marks)

Nitrogen gas in a sealed flask is at a temperature of $300\ \text{K}$300 K. A single nitrogen molecule has a mass of $4.65 \times 10^{-26}\ \text{kg}$4.65×10−26 kg. The gas may be treated as ideal.

Take the Boltzmann constant $k = 1.38 \times 10^{-23}\ \text{J K}^{-1}$k=1.38×10−23 J K−1.

(a) Calculate the mean (random) translational kinetic energy of a nitrogen molecule at this temperature. (2 marks)

(b) Hence calculate the root-mean-square (r.m.s.) speed of the nitrogen molecules. (2 marks)

The behaviour of a substance can be described in terms of the energies of its molecules.

(a) Define the internal energy of a system. (2 marks)

(b) State what is meant by absolute zero in terms of the internal energy of a substance. (1 mark)