18 8 A student investigated the rate at which a hot liquid transfers thermal energy to the surroundings. He placed hot water in a Pyrex beaker and measured the temperature of the water using a liquid-in-glass thermometer. He obtained the following data for the temperature θ of the water at times t. He measured t using a stopwatch. t / s θ / °C 0 95 120 87 240 81 360 76 480 71 temperature of surroundings = 23 °C Theory suggests that a liquid transfers internal energy to the surroundings at a rate proportional to the temperature difference Δθ between the liquid and the surroundings. This leads to the expression Δθ = Δθ0e −bt where b is a constant and Δθ0 is the initial temperature difference. (a) Explain why a graph of ln Δθ against t should be a straight line. (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (b) (i) Plot a graph of ln Δθ against t on the grid opposite. Use the columns provided in the table to show any processed data. (5) 19 Turn over 20 (ii) Determine the value of b. (3) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. b = ....................................................... (c) The student suggested that the experiment would have been more accurate if a temperature sensor and data logger had been used to collect the data. Assess the validity of the student’s suggestion. (4) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 8 = 14 marks) 21 Turn over BLANK PAGE