Chapter 17: Problem 17
A glass flask whose volume is 1000.00 cm\(^3\) at 0.0\(^\circ\)C is completely filled with mercury at this temperature. When flask and mercury are warmed to 55.0\(^\circ\)C, 8.95 cm\(^3\) of mercury overflow. If the coefficient of volume expansion of mercury is \(18.0 \times 10{^-}{^5} K{^-}{^1}\), compute the coefficient of volume expansion of the glass.
Short Answer
Step by step solution
Understand the Provided Information
Calculate the Expansion of Mercury
Substitute Values to Find Change in Mercury Volume
Calculate the Numerical Result for Mercury Expansion
Determine Flask's Expansion
Calculate the Coefficient of Volume Expansion of the Glass
Solve the Expression for the Glass Expansion Coefficient
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Thermal Expansion
In the case of this exercise, the glass flask and the mercury inside it both experience thermal expansion. Since the coefficient of volume expansion differs between different materials, not all components expand at the same rate when subjected to the same temperature change. This differing expansion is the reason we observe overflow in the mercury from the flask.
- The coefficient of volume expansion (\(\beta)\) is a property that quantifies how much a material's volume changes per degree change in temperature.
- In the formula \(\Delta V = V_0 \beta \Delta T\), \\(\Delta V\) is the change in volume, \\(V_0\) is the initial volume, \\(\beta\) is the coefficient of volume expansion, and\(\Delta T\) is the temperature change.
Physics Problem Solving
The step-by-step process follows a structured approach:
- Understand the problem: Identify what is known and what needs to be found. Here, we know the initial volume of the flask and mercury, the overflow amount, and the coefficient of mercury's expansion.
- Calculate known variables: Calculate the change in volume (\(\Delta V)\) for mercury using the formula \\(\Delta V = V_0 \beta \Delta T\). This helps determine how much the volume of mercury increases when heated.
- Analyze results: By calculating the difference in volume expansions between the mercury and the flask, you find how much the mercury overflows due to expansion.
- Solve for unknowns: Determine the coefficient of volume expansion of the glass by rearranging formulas accordingly and substituting known quantities.
Temperature Change
Understanding \(\Delta T\) (the change in temperature) is key in applying the thermal expansion formulas as it helps quantify how significant the expansion will be.
- \(\Delta T\) for our exercise is 55.0 K, calculated simply as \\(55.0 - 0.0\).
- Temperature changes affect different materials in distinct ways depending on their expansion coefficients.
- Accurate measurement of temperature change ensures precise assessments of how materials like glass and mercury will react when heated.