5. A thermometer and an electrical heater are inserted into small holes in a solid aluminium block.

A thermometer and an electrical heater are inserted into small holes in a solid aluminium block. The heater is turned on at time t = 0. The graph shows the variation of the temperature q of the block with time t.

(a) (i) On the graph, draw the line of best-fit for the data. [1]
(ii) Estimate the initial temperature of the block.

(b) Suggest why the temperature of the block approaches a constant value.

(c) When the temperature has reached a constant value, the heater is turned off. The graph shows the variation of the temperature q of the block with time t. Show that the initial rate of change of the temperature of the block is approximately -4.0 K/ min .

(d) The power of the heater is 52W. The mass of the block is 0.85kg. Determine the specific heat capacity of aluminium.

(e) The percentage uncertainty in the rate of change in (c) is 4%. The percentage uncertainty in the power of the heater is 3% and that in the mass of the block is 1%.
(i) Estimate the absolute uncertainty in the specific heat capacity of aluminium.
(ii) Write down the value of the specific heat capacity of aluminium, its uncertainty, and its unit. Give your answer to an appropriate number of significant figures.

Overview:
This problem is taken from the past papers of IBDP Physics curriculum, focusing on Data Analysis, that is related to thermal physics and the relationship between heat energy, temperature, and specific heat capacity. It involves analyzing a temperature-time graph, interpreting the heater's power, and calculating specific heat capacity with uncertainties. These types of problems are crucial for understanding how thermal energy is transferred and calculated in real-world scenarios.

Core Concepts:
To solve this problem, students should have a good grasp of the following:

Heat and temperature (difference between them).
Specific heat capacity and its calculation.
Graph analysis for rates of temperature change.
Understanding of uncertainty calculations and how they affect final results.
These concepts are central to IBDP Physics and commonly appear in exam questions on thermal properties of matter.

About the Homework Series:
Each week, I post 5 IBDP Physics problems to help students develop problem-solving skills. Solve one problem per day, and come back at 5 PM for the solution. This structured approach is perfect for revising key Physics concepts.

For more detailed practice and organized learning, visit my Homework Portal, where problems are sorted by topics, ensuring comprehensive exam preparation.

Hashtags:
#IBPhysics #IBDPPhysics #ThermalPhysics #SpecificHeatCapacity #PhysicsGraphAnalysis #UncertaintyCalculations #PhysicsHomework #PhysicsProblemSolving #IBPhysicsSolutions #PhysicsDaily #PhysicsLearning