Question 1
1
A light spring is suspended from a fixed point. A bar magnet is attached to the end of the spring, as shown in Fig. 1.1. In order to shield the magnet from draughts, a cardboard cup is placed around the magnet but does not touch it. The magnet is displaced vertically and then released. The variation with time t of the vertical displacement y of the magnet is shown in Fig. 1.2. The mass of the magnet is 130 g .
structured0 marks
Question 1(c)
1(c)
The mass of the aluminium cup in (b) is 6.2 g . The specific heat capacity of aluminium is \(910 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}\). The energy in (b)(ii) is transferred to the cup as thermal energy. Calculate the mean rise in temperature of the cup. temperature rise = Please turn over for Question 2.
Easystructured0 marks
Answer
\(q=m c \Delta \theta\) \(4.8 \times 10^{-3}=6.2 \times 10^{-3} \times 910 \times \Delta \theta \quad\) C1 \(\Delta \theta=8.5 \times 10^{-4} \mathrm{~K}\)
Question 1
1
Fig. 1.1 shows a small solid metal cylinder of mass m, length L and diameter d. The cylinder is heated to a uniform temperature. The cylinder is then removed from the heat source and the cylinder is wrapped in an insulating material. The temperature of the room is \(T_{\mathrm{R}}\). At time t after the cylinder starts to cool, the surface temperature of the cylinder is \(T_{\mathrm{C}}\). It is suggested that \(T_{\mathrm{C}}\) is related to t by the relationship where A is the total surface area of the cylinder, c is the specific heat capacity of the metal, and U and Z are constants. Plan a laboratory experiment to test the relationship between \(T_{\mathrm{C}}\) and t. Draw a diagram showing the arrangement of your equipment. Explain how the results could be used to determine values for U and Z. In your plan you should include: - the procedure to be followed - the measurements to be taken - the control of variables - the analysis of the data - any safety precautions to be taken. Diagram
Hard15 marks
Answer
Defining the problem t is the independent variable and \(T_{\mathrm{c}}\) is the dependent variable or vary t and measure \(T_{\mathrm{c}}\) keep \(T_{\mathrm{R}}\) constant Methods of data collection labelled diagram of workable experiment including: - solid cylinder cooling - insulation surrounding all of the cylinder - thermometer touching cylinder inside insulation - insulation and thermometer labelled method to heat the cylinder uniformly, e.g. place in oven/immerse in hot water or diagram showing cylinder in oven or hot water method to determine time t, e.g. stopwatch or temperature sensor connected to a data logger method to measure L e.g. use a ruler/calipers/micrometer and method to measure d e.g. use calipers/micrometer Method of Analysis plot a graph of \(\ln \left(T_{\mathrm{C}}-T_{\mathrm{R}}\right)\) against t or equivalent \(U=-\frac{m c \times \text { gradient }}{A}\) \(Z=\mathrm{e}^{y \text {-intercept }}\) 1 Additional detail including safety considerations D1 precaution to prevent burns or use of hot cylinder / oven / hot water e.g. use of gloves, use of tongs D2 keep thickness of the insulating material constant (for each \(T_{\mathrm{C}}\) ) D3 method to measure m, e.g. use a (top-pan) balance D4 for water bath/oven methods, wait for initial temperature of the cylinder to become uniform or constant throughout the cylinder D5 (surface) \(A=\pi d L+\frac{\pi d^{2}}{2}\) or \(\pi d L+2\left(\frac{\pi d^{2}}{4}\right)\) D6 repeat measurements of d along the length of the cylinder / in different directions and determine the average value of d D7 description of how c is determined from a separate experiment by heating the cylinder using electrical heater and \[ c=\frac{\Delta E}{m \Delta \theta} \] D8 method of determining energy supplied to electrical heater to determine c, e.g. use of joulemeter for \(\Delta E\) or electrical method using ammeter and voltmeter to determine I V t D9 use several temperature sensors and determine the average \(T_{\mathrm{C}}\) D10 relationship valid if a straight line is produced (with y-intercept \(=\ln Z\) ) Do not accept line passing through the origin.
Question 3
3
8 marks
Question 3(a)
3(a)
Define specific latent heat.
Easystructured2 marks
Answer
(numerically equal to) quantity of heat/(thermal) energy to change state/phase of unit mass at constant temperature (allow 1/2 for definition restricted to fusion or vaporisation)
Question 3(b)
3(b)
A beaker containing a liquid is placed on a balance, as shown in Fig. 3.1. A heater of power 110 W is immersed in the liquid. The heater is switched on and, when the liquid is boiling, balance readings m are taken at corresponding times t. A graph of the variation with time t of the balance reading m is shown in Fig. 3.2.
structured6 marks
Question 3(b)(i)
3(b)(i)
State the feature of Fig. 3.2 which suggests that the liquid is boiling at a steady rate.
Easystructured1 marks
Answer
constant gradient/straight line (allow linear/constant slope)
Question 3(b)(ii)
3(b)(ii)
Use data from Fig. 3.2 to determine a value for the specific latent heat L of vaporisation of the liquid.
Mediumstructured3 marks
Answer
Pt =m L or power = gradient × L use of gradient of graph (or two points separated by at least 3.5 minutes) \(110 \times 60=L \times(372-325) \times 10^{-3} / 7.0\) \(L=9.80 \times 10^{5} \mathrm{Jkg}^{-1}\) (accept 2 s.f.) (allow 9.8 to 9.9 rounded to 2 s.f.)
Question 3(b)(iii)
3(b)(iii)
State, with a reason, whether the value determined in (ii) is likely to be an overestimate or an underestimate of the normally accepted value for the specific latent heat of vaporisation of the liquid.
Mediumstructured2 marks
Answer
some energy/heat is lost to the surroundings or vapour condenses on sides so value is an overestimate
Question 3
3
4 marks
Question 3(a)
3(a)
Define specific latent heat.
Easystructured2 marks
Answer
(numerically equal to) quantity of (thermal) energy/heat to change state/phase of unit mass at constant temperature (allow 1/2 for definition restricted to fusion or vaporisation)
Question 3(b)
3(b)
An electrical heater is immersed in some melting ice that is contained in a funnel, as shown in Fig. 3.1. The heater is switched on and, when the ice is melting at a constant rate, the mass m of ice melted in 5.0 minutes is noted, together with the power P of the heater. The power P of the heater is then increased. A new reading for the mass m of ice melted in 5.0 minutes is recorded when the ice is melting at a constant rate. Data for the power P and the mass m are shown in Fig. 3.2.
structured2 marks
Question 3(b)(i)
3(b)(i)
Complete Fig. 3.2 to determine the mass melted per second for each power of the heater.
Mediumstructured2 marks
Answer
at 70 W , mass \(\mathrm{s}^{-1}=0.26 \mathrm{~g} \mathrm{~s}^{-1}\) at 110 W , mass \(\mathrm{s}^{-1}=0.38 \mathrm{~g} \mathrm{~s}^{-1}\)
Question 3(b)(ii)
3(b)(ii)
Use the data in the completed Fig. 3.2 to determine
Mediumstructured0 marks
Answer
1. P+h=m L or substitution of one set of values (110-70)=(0.38-0.26) L \[ L=330 \mathrm{Jg}^{-1} \] C1 C1 A1 2. either \(70+h=0.26 \times 330\) \[ \text { or } 110+h=0.38 \times 330 \] \(h=17 / 16 / 15 \mathrm{~W}\) C1 A1