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Ch 17: Temperature and Heat
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 17, Problem 18

A steel tank is completely filled with 1.90 m3 of ethanol when both the tank and the ethanol are at 32.0°C. When the tank and its contents have cooled to 18.0°C, what additional volume of ethanol can be put into the tank?

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1
Understand the problem: We need to find out how much additional ethanol can be added to the tank when both the tank and ethanol cool down from 32.0°C to 18.0°C. This involves understanding the concept of thermal expansion.
Identify the relevant formulas: The volume change due to temperature change can be calculated using the formula for volumetric thermal expansion: ΔV=VβΔT, where ΔV is the change in volume, V is the initial volume, β is the coefficient of volumetric expansion, and ΔT is the change in temperature.
Determine the coefficients of volumetric expansion: Look up the coefficient of volumetric expansion for ethanol and steel. These values are typically found in physics textbooks or reliable online resources. For ethanol, β is approximately 1.12×104 per °C, and for steel, it is approximately 3.6×105 per °C.
Calculate the change in volume for both the ethanol and the steel tank: Use the formula ΔV=VβΔT for both materials. The initial volume V is 1.90 m³, and the temperature change ΔT is 32.0-18.0 °C.
Determine the additional volume of ethanol that can be added: Subtract the volume change of the steel tank from the volume change of the ethanol to find out how much more ethanol can be added to the tank after cooling.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Thermal Expansion

Thermal expansion refers to the tendency of matter to change in volume in response to a change in temperature. For liquids like ethanol, the volume decreases as the temperature drops, which is crucial for understanding how much additional ethanol can be added when the temperature decreases from 32.0°C to 18.0°C.
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Volume Thermal Expansion

Coefficient of Volume Expansion

The coefficient of volume expansion quantifies how much a substance's volume changes per degree change in temperature. For ethanol, this coefficient helps calculate the change in volume as the temperature drops, allowing us to determine the additional volume that can be added to the tank.
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Volume Thermal Expansion

Temperature Change and Volume Calculation

Understanding the relationship between temperature change and volume calculation is essential for solving this problem. By applying the formula for volume change, which involves the initial volume, the coefficient of volume expansion, and the temperature change, we can calculate the new volume of ethanol at 18.0°C and determine the additional volume that can be added.
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Specific Heat & Temperature Changes
Related Practice
Textbook Question

A 6.00-kg piece of solid copper metal at an initial temperature T is placed with 2.00 kg of ice that is initially at -20.0°C. The ice is in an insulated container of negligible mass and no heat is exchanged with the surroundings. After thermal equilibrium is reached, there is 1.20 kg of ice and 0.80 kg of liquid water. What was the initial temperature of the piece of copper?

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In an effort to stay awake for an all-night study session, a student makes a cup of coffee by first placing a 200-W electric immersion heater in 0.320 kg of water. How much time is required? Assume that all of the heater's power goes into heating the water.

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