GRADE 12 PHYSICS ASSESSMENT 2
PART B:
EXTENDED RESPONSE QUESTIONS
ASSESSMENT BOOKLET
(20 MARKS)
Explain your answers in detail and in complete sentences. Where mathematical calculations are necessary, include all calculation steps in your answer(s). These will assist the tutor/marker in evaluating your complete solution. Write your answers in the space provided next to the questions.
QUESTION 1
(5 marks)
A liquid X at 25°C is poured to a height of 40cm in a thin capillary tube of length 70cm and diameter of 1cm. Assume that the volume of the capillary tube does not change with temperature.
a) Find the initial volume of the liquid in cm³.
b) The temperature of the liquid is reduced by 10°C causing the liquid to reduce in height to 37cm. Find the volume coefficient of thermal expansion (B) of this liquid.
c) At the initial height of 40cm and temperature of 25°C, what change in temperature (ΔT) is needed for the liquid to rise to a height of 49cm?
Answer (2)
Calculate the initial volume using the formula for the volume of a cylinder: V i = π r 2 h i ≈ 31.42 cm 3 .
Determine the final volume after the temperature reduction: V f = π r 2 h f ≈ 29.06 cm 3 .
Calculate the volume coefficient of thermal expansion using the formula V f = V i ( 1 + β Δ T ) , resulting in β ≈ 0.0075 /°C .
Find the change in temperature needed to reach the target height using V t = V i ( 1 + β Δ T ) , which gives Δ T ≈ 30 °C .
Explanation
Problem Analysis We are given a problem involving the thermal expansion of a liquid in a capillary tube. We need to find the initial volume of the liquid, the volume coefficient of thermal expansion, and the change in temperature required for the liquid to reach a specific height.
Calculating Initial Volume a) To find the initial volume of the liquid, we use the formula for the volume of a cylinder, V = π r 2 h , where r is the radius and h is the height. Given the diameter is 1 cm, the radius is r = 0.5 cm, and the initial height is h i = 40 cm. Thus, the initial volume V i is: V i = π ( 0.5 ) 2 ( 40 ) V i = π ( 0.25 ) ( 40 ) V i = 10 π ≈ 31.42 cm 3
Calculating Volume Coefficient of Thermal Expansion b) To find the volume coefficient of thermal expansion ( β ), we use the formula for volume expansion: V f = V i ( 1 + β Δ T ) , where V f is the final volume, V i is the initial volume, and Δ T is the change in temperature. We are given that the temperature is reduced by 10°C, so Δ T = − 10° C , and the final height is h f = 37 cm. First, we calculate the final volume: V f = π r 2 h f = π ( 0.5 ) 2 ( 37 ) = π ( 0.25 ) ( 37 ) = 9.25 π ≈ 29.06 cm 3 Now, we can solve for β :
V f = V i ( 1 + β Δ T ) 29.06 = 31.42 ( 1 + β ( − 10 )) 31.42 29.06 = 1 − 10 β 0.9249 = 1 − 10 β 10 β = 1 − 0.9249 10 β = 0.0751 β = 10 0.0751 = 0.00751 /°C So, the volume coefficient of thermal expansion is approximately 0.0075 /°C .
Calculating the Change in Temperature c) To find the change in temperature ( Δ T ) needed for the liquid to rise to a height of 49 cm, we use the same volume expansion formula: V t = V i ( 1 + β Δ T ) , where V t is the target volume, V i is the initial volume, and β is the volume coefficient of thermal expansion. The target height is h t = 49 cm. First, we calculate the target volume: V t = π r 2 h t = π ( 0.5 ) 2 ( 49 ) = π ( 0.25 ) ( 49 ) = 12.25 π ≈ 38.48 cm 3 Now, we can solve for Δ T :
V t = V i ( 1 + β Δ T ) 38.48 = 31.42 ( 1 + 0.0075Δ T ) 31.42 38.48 = 1 + 0.0075Δ T 1.2247 = 1 + 0.0075Δ T 0.0075Δ T = 0.2247 Δ T = 0.0075 0.2247 = 29.96 ≈ 30 °C So, the change in temperature needed is approximately 30 °C .
Final Answer a) The initial volume of the liquid is approximately 31.42 cm 3 .
b) The volume coefficient of thermal expansion is approximately 0.0075 /°C .
c) The change in temperature needed for the liquid to rise to a height of 49 cm is approximately 30 °C .
Examples
Understanding thermal expansion is crucial in many real-world applications. For instance, bridges and buildings are designed with expansion joints to accommodate changes in temperature, preventing structural damage. In the kitchen, the slight expansion of liquids when heated is a factor in cooking and baking, affecting the final volume and consistency of dishes. Even in the automotive industry, the thermal expansion of engine components is considered to ensure optimal performance and prevent overheating.
The initial volume of the liquid is approximately 31.42 cm³. The volume coefficient of thermal expansion is approximately 0.0075 /°C, and to raise the liquid to a height of 49 cm, a temperature change of about 30 °C is needed.
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