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Ch 17: Temperature and Heat
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 17: Temperature and HeatProblem 18
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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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 1.12×10⁻4 per °C, and for steel, it is approximately 3.6×10⁻5 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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Textbook Question

One of the tallest buildings in the world is the Taipei 101 in Taiwan, at a height of 1671 feet. Assume that this height was measured on a cool spring day when the temperature was 15.5°C. You could use the building as a sort of giant thermometer on a hot summer day by carefully measuring its height. Suppose you do this and discover that the Taipei 101 is 0.471 foot taller than its official height. What is the temperature, assuming that the building is in thermal equilibrium with the air and that its entire frame is made of steel?

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Textbook Question

Steel train rails are laid in 12.0-m-long segments placed end to end. The rails are laid on a winter day when their temperature is -9.0°C. How much space must be left between adjacent rails if they are just to touch on a summer day when their temperature is 33.0°C?

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Textbook Question

As a new mechanical engineer for Engines Inc., you have been assigned to design brass pistons to slide inside steel cylinders. The engines in which these pistons will be used will operate between 20.0°C and 150.0°C. Assume that the coefficients of expansion are constant over this temperature range. If the piston just fits inside the chamber at 20.0°C, will the engines be able to run at higher temperatures? Explain.

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Textbook Question

A brass rod is 185 cm long and 1.60 cm in diameter. What force must be applied to each end of the rod to prevent it from contracting when it is cooled from 120.0°C to 10.0°C?

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Textbook Question

A geodesic dome constructed with an aluminum framework is a nearly perfect hemisphere; its diameter measures 55.0 m on a winter day at a temperature of -15°C. How much more interior space does the dome have in the summer, when the temperature is 35°C?

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