An electric generating plant boils water to produce high...

An electric generating plant boils water to produce high pressure steam. The steam spins a turbine that is connected to the generator. a. How many liters of water must be boiled to fill a $5.0 \mathrm{m}^{3}$ boiler with 50 atm of steam at $400^{\circ} \mathrm{C} ?$ b. The steam has dropped to 2.0 atm pressure at $150^{\circ} \mathrm{C}$ as it exits the turbine. How much volume does it now occupy?

An electric generating plant boils water to produce high pressure steam. The steam spins a turbine that is connected to the generator.
a. How many liters of water must be boiled to fill a $5.0 \mathrm{m}^{3}$ boiler with 50 atm of steam at $400^{\circ} \mathrm{C} ?$
b. The steam has dropped to 2.0 atm pressure at $150^{\circ} \mathrm{C}$ as it exits the turbine. How much volume does it now occupy?

Key Concepts

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, is a fundamental principle in thermodynamics that relates the pressure (P), volume (V), temperature (T), and number of moles (n) of a gas using the gas constant (R). This relationship allows for the determination of any one of these variables when the others are known and is particularly useful in computing the required amount of gas or changes in its state under different conditions.

Phase Change from Liquid to Gas

The phase transition where water converts from liquid to steam is characterized by a dramatic increase in volume. This process, driven by the addition of thermal energy, is central to power generation methods where a relatively small volume of liquid water creates a much larger volume of high-pressure steam used to drive turbines.

Mole Concept and Mass-Volume Conversions

The mole concept is essential for relating the mass of a substance to the number of particles it contains. In problems involving steam generation, converting the mass of water to moles using its molar mass—and considering the density of water—enables the application of the ideal gas law to determine the corresponding gas volume at specified pressures and temperatures.

Temperature Conversion

In thermodynamic calculations, temperatures must be expressed on an absolute scale, typically Kelvin. Converting Celsius to Kelvin is a necessary step to accurately apply the ideal gas law, as the temperature term in the equation must reflect an absolute measure of thermal energy.

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