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Ch 18: A Macroscopic Description of Matter
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 18, Problem 51a

An electric generating plant boils water to produce high-pressure steam. The steam spins a turbine that is connected to the generator. How many liters of water must be boiled to fill a 5.0 m3 boiler with 50 atm of steam at 400°C?

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Step 1: Recognize that this problem involves the Ideal Gas Law, which is expressed as PV=nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin.
Step 2: Convert the given temperature from Celsius to Kelvin using the formula Tk=Tc+273.15. For 400°C, the temperature in Kelvin is 400+273.15.
Step 3: Use the Ideal Gas Law to calculate the number of moles of steam in the boiler. Rearrange the formula to solve for n: n=PV/RT. Substitute the values: P = 50 atm, V = 5.0 m³, R = 0.0821 L·atm/(mol·K), and T = the temperature in Kelvin from Step 2.
Step 4: Determine the mass of water required to produce the calculated number of moles of steam. Use the molar mass of water, which is approximately 18.015 g/mol. The mass is given by m=nM, where M is the molar mass.
Step 5: Convert the mass of water into liters. Since the density of water is approximately 1 g/mL, the volume in liters is numerically equal to the mass in kilograms. Divide the mass in grams by 1000 to find the volume in liters.

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Key Concepts

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

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for understanding how gases behave under different conditions, particularly in calculating the amount of steam produced from boiling water in a closed system like a boiler.
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Phase Change and Latent Heat

Phase change refers to the transition of a substance from one state of matter to another, such as from liquid to gas. The latent heat of vaporization is the energy required to convert a unit mass of a liquid into vapor without a change in temperature, which is crucial for determining how much energy is needed to boil water in the boiler.
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Steam Properties

Steam, as a gas, has specific properties that depend on its pressure and temperature. At 50 atm and 400°C, steam behaves differently than at standard atmospheric conditions, affecting calculations related to volume and mass. Understanding these properties is vital for determining how much water is needed to produce the desired amount of steam.
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Related Practice
Textbook Question

The 3.0-m-long pipe in FIGURE P18.49 is closed at the top end. It is slowly pushed straight down into the water until the top end of the pipe is level with the water's surface. What is the length L of the trapped volume of air?

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Textbook Question

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Textbook Question

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