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Chapter 17: Problem 2

How is the sign of \(q\), heat, defined? How does it relate to the total energy of the system?

Short Answer

Expert verified
The sign of \(q\) shows heat flow direction: positive for absorbed heat, negative for released. It affects the system's internal energy change.

Step by step solution

01

Understanding Heat (q)

The sign of the heat, represented by \(q\), indicates the direction of heat flow in a thermodynamic process. It is positive if heat is absorbed by the system from the surroundings, making the process endothermic. Conversely, it is negative if heat is released by the system to the surroundings, making the process exothermic.
02

Relation to Total Energy of System

The total energy of a system is represented by the internal energy change \( \Delta U \). According to the first law of thermodynamics, \( \Delta U = q + w \), where \(w\) is the work done by or on the system. A positive \(q\) increases the total energy of the system (as heat is absorbed), whereas a negative \(q\) decreases it (as heat is released).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Heat Flow
In thermodynamics, heat flow is an essential concept that refers to the movement of heat energy from one place to another. Heat naturally flows from hotter objects to cooler ones until thermal equilibrium is reached. This concept is crucial in understanding how energy is transferred in various processes.
  • Directionality: Heat flows in a particular direction, depending on the temperature gradient. It moves from regions of high temperature to regions of low temperature.
  • Measurement: Heat flow is measured in terms of energy per unit time. Common units include Joules per second (Watts).
Understanding the direction and extent of heat flow helps in analyzing how energy transfer affects a system, influencing various physical and chemical changes.
Endothermic Process
An endothermic process is one in which the system absorbs heat from its surroundings. This type of process results in a positive sign for heat ( q). When a system undergoes an endothermic reaction, the surroundings effectively provide energy to the system, increasing its internal energy.
  • Examples: Melting ice, boiling water, and photosynthesis are all common examples of endothermic processes.
  • Energy Transformation: The absorbed heat generally results in phase changes, chemical reactions, or temperature increases within the system.
In these processes, temperature changes are often observable, and additional energy input is frequently required to sustain them.
Exothermic Process
An exothermic process is characterized by the release of heat energy from the system into the surroundings. In this case, the symbol for heat ( q) is negative, indicating an outward flow of energy. This type of process often involves the transformation of stored chemical energy into heat energy.
  • Examples: Combustion, freezing water, and cellular respiration are typical exothermic reactions.
  • Energy Effects: As energy is released, there is usually a temperature increase in the surroundings, making these processes observable through heat emission.
Exothermic processes often occur spontaneously, as they lead to a decrease in the system's internal energy, contributing to system stability.

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Most popular questions from this chapter

A A \(220-\mathrm{ft}^{3}\) sample of gas at standard temperature and pressure is compressed into a cylinder, where it exerts pressure of 2000 psi. Calculate the work (in J) performed when this gas expands isothermally against an opposing pressure of 1.0 atm. (The amount of work that can be done is equivalent to the destructive force of about \(1 / 4 \mathrm{lb}\) of dynamite, giving you an idea of how potentially destructive compressed gas cylinders can be if improperly handled!)

Calculate the work performed if a balloon contracts from \(12.90 \mathrm{~L}\) to \(788 \mathrm{~mL}\) because of an external pressure of \(3.70 \mathrm{~atm} .\)

A colleague states, "Since there is no detectable chemical change when methane \(\left(\mathrm{CH}_{4}\right)\) and oxygen mix, the reaction of these two substances is not spontaneous." Explain what is wrong with this statement.

Calculate \(w\) for the following reactions that occur at 298 \(\mathrm{K}\) and 1 atm pressure. Consider only \(P V\) work from the change in volume of gas, and assume that the gases are ideal and the chemical equation represents amounts in moles. (a) \(\mathrm{CO}_{2}(\mathrm{~g})+\mathrm{NaOH}(\mathrm{s}) \rightarrow \mathrm{NaHCO}_{3}(\mathrm{~s})\) (b) \(3 \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{O}_{3}(\mathrm{~g})\)

Calculate \(w\) for the following reactions that occur at \(298 \mathrm{~K}\) and 1 atm pressure. Consider only \(P V\) work from the change in volume of gas, and assume that the gases are ideal and the chemical equation represents amounts in moles. (a) \(\mathrm{Fe}(\mathrm{s})+5 \mathrm{CO}(\mathrm{g}) \rightarrow \mathrm{Fe}(\mathrm{CO})_{5}(\mathrm{~g})\) (b) \(6 \mathrm{CO}_{2}(\mathrm{~g})+6 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{~s})+6 \mathrm{O}_{2}(\mathrm{~g})\)
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