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Chapter 6: Problem 11

Consider an airplane trip from Chicago, Illinois, to Denver, Colorado. List some path-dependent functions and some state functions for the plane trip.

Short Answer

Expert verified
Some path-dependent functions for an airplane trip from Chicago to Denver include total distance traveled, fuel consumption, and total flight time. These quantities depend on the specific flight route and other factors such as wind conditions and delays. Some state functions for the trip include altitude difference, latitude and longitude, and temperature difference between the departure and arrival cities. These properties depend only on the initial and final states of the system, regardless of the path taken during the process.

Step by step solution

01

Understanding path-dependent functions

Path-dependent functions are properties or quantities that depend on the specific path taken during a process. In other words, the value of a path-dependent function depends on the detailed history of the system, such as the route of the trip. For the airplane trip, examples of path-dependent functions can include distance traveled, fuel consumption, and flight time.
02

List some path-dependent functions

Here are some examples of path-dependent functions for an airplane trip from Chicago to Denver: 1. Total distance traveled (in miles or kilometers): The exact distance traveled will depend on the specific flight route. 2. Fuel consumption (in gallons or liters): The fuel consumption of the airplane will depend on factors such as flight path, altitude, wind conditions, and any detours or stopovers. 3. Total flight time (in hours or minutes): The duration of the trip will depend on the route taken and factors like air traffic and other delays.
03

Understanding state functions

State functions are properties that depend only on the initial and final states of a system, regardless of the path taken during a process. In contrast to path-dependent functions, state functions do not depend on the detailed history of the system. For the airplane trip, examples of state functions can include altitude, latitude and longitude, and temperature difference between the departure and arrival cities.
04

List some state functions

Here are some examples of state functions for an airplane trip from Chicago to Denver: 1. Altitude difference (in feet or meters): This would be the difference in elevation between the airports in Chicago and Denver. This is a state function because it depends only on the initial and final elevations, not on the detailed flight path. 2. Latitude and longitude: These coordinates define the locations of the departure and arrival airports, and are independent of the flight route taken. 3. Temperature difference (in degrees Celsius or Fahrenheit): The temperature difference between the departure city (Chicago) and the arrival city (Denver) is independent of the flight path and depends only on the ambient temperatures of the two cities.

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Most popular questions from this chapter

Quinone is an important type of molecule that is involved in photosynthesis. The transport of electrons mediated by quinone in certain enzymes allows plants to take water, carbon dioxide, and the energy of sunlight to create glucose. A \(0.1964-\mathrm{g}\) sample of quinone \(\left(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{O}_{2}\right)\) is burned in a bomb calorimeter with a heat capacity of \(1.56 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\). The temperature of the calorimeter increases by \(3.2^{\circ} \mathrm{C}\). Calculate the energy of combustion of quinone per gram and per mole.

The bomb calorimeter in Exercise 108 is filled with \(987 \mathrm{~g}\) water. The initial temperature of the calorimeter contents is \(23.32^{\circ} \mathrm{C}\). A \(1.056-\mathrm{g}\) sample of benzoic acid \(\left(\Delta E_{\text {comb }}=-26.42 \mathrm{~kJ} / \mathrm{g}\right)\) is combusted in the calorimeter. What is the final temperature of the calorimeter contents?

A sample consisting of \(22.7 \mathrm{~g}\) of a nongaseous, unstable compound \(\mathrm{X}\) is placed inside a metal cylinder with a radius of \(8.00 \mathrm{~cm}\), and a piston is carefully placed on the surface of the compound so that, for all practical purposes, the distance between the bottom of the cylinder and the piston is zero. (A hole in the piston allows trapped air to escape as the piston is placed on the compound; then this hole is plugged so that nothing inside the cylinder can escape.) The piston-and-cylinder apparatus is carefully placed in \(10.00 \mathrm{~kg}\) water at \(25.00^{\circ} \mathrm{C}\). The barometric pressure is 778 torr. When the compound spontaneously decomposes, the piston moves up, the temperature of the water reaches a maximum of \(29.52^{\circ} \mathrm{C}\), and then it gradually decreases as the water loses heat to the surrounding air. The distance between the piston and the bottom of the cylinder, at the maximum temperature, is \(59.8 \mathrm{~cm}\). Chemical analysis shows that the cylinder contains \(0.300 \mathrm{~mol}\) carbon dioxide, \(0.250\) mol liquid water, \(0.025\) mol oxygen gas, and an undetermined amount of a gaseous element \(\mathrm{A}\). It is known that the enthalpy change for the decomposition of \(X\), according to the reaction described above, is \(-1893\) \(\mathrm{kJ} / \mathrm{mol} \mathrm{X}\). The standard enthalpies of formation for gaseous carbon dioxide and liquid water are \(-393.5 \mathrm{~kJ} / \mathrm{mol}\) and \(-286 \mathrm{~kJ} / \mathrm{mol}\), respectively. The heat capacity for water is \(4.184 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\). The conversion factor between \(\mathrm{L} \cdot \mathrm{atm}\) and \(\mathrm{J}\) can be determined from the two values for the gas constant \(R\), namely, \(0.08206 \mathrm{~L}\). \(\mathrm{atm} / \mathrm{K} \cdot \mathrm{mol}\) and \(8.3145 \mathrm{~J} / \mathrm{K} \cdot \mathrm{mol}\). The vapor pressure of water at \(29.5^{\circ} \mathrm{C}\) is 31 torr. Assume that the heat capacity of the pistonand-cylinder apparatus is negligible and that the piston has negligible mass. Given the preceding information, determine a. The formula for \(\mathrm{X}\). b. The pressure-volume work (in \(\mathrm{kJ}\) ) for the decomposition of the \(22.7-\mathrm{g}\) sample of \(\mathrm{X}\). c. The molar change in internal energy for the decomposition of \(X\) and the approximate standard enthalpy of formation for \(X\).

The heat capacity of a bomb calorimeter was determined by burning \(6.79 \mathrm{~g}\) methane (energy of combustion \(=-802 \mathrm{~kJ} / \mathrm{mol} \mathrm{CH}_{4}\) ) in the bomb. The temperature changed by \(10.8^{\circ} \mathrm{C}\). a. What is the heat capacity of the bomb? b. A \(12.6-\mathrm{g}\) sample of acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}\), produced a temperature increase of \(16.9^{\circ} \mathrm{C}\) in the same calorimeter. What is the energy of combustion of acetylene (in \(\mathrm{kJ} / \mathrm{mol}\) )?

A gas absorbs \(45 \mathrm{~kJ}\) of heat and does \(29 \mathrm{~kJ}\) of work. Calculate \(\Delta E\).
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