5.1 Work and Heat

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5.1.1 Introduction

I Thermodynamics: the study of transformations of energy between work and heat

1. heat and work are two different ways energy can be transferred

II The study of thermodynamics can be divided into two regions of interest:

1. system: the region of interest

2. surroundings: everything else

3. universe: the system and the surroundings

III The system and the surroundings can also be classified by what can be transferred:

1. open system: matter and energy are exchangeable between the system and surroundings

2. closed system: matter is not exchangeable, but energy is exchangeable

3. isolated system: both matter and energy are nonexchangeable with the surroundings

IV there are terms that indicate specific conditions of a system:

1. isothermal: the temperature of the system stays constant

2. isobaric: the pressure of the system stays constant

3. isochoric: the volume of the system stays constant

V Energy: the capacity to do work or to heat an object

1. A body may have energy by virtue of either its motion or its position

   1. kinetic energy ($\textrm{E}_{k}$) is the energy of a body due to its motion

   2. potential energy ($\textrm{E}_{p}$) is the energy of a body due to its position

2. the total store of energy in a system is called its internal energy ($\textrm{U}$)

   1. the internal energy cannot be measured or calculated.

   2. instead, the changes of internal energy ($\Delta \textrm{U}$) is measured.

VI Thermodynamics in chemistry is often focused on the system; if not explicitly stated, assume everything is referring to the system. (e.g. $\textrm{q}$ is equivalent to $\textrm{q}_{\textrm{sys}}$)

5.1.2 Work

VII work ($\textrm{w}$) is the process of achieving motion against an opposing force

$\textrm{w} = \textrm{F} \textrm {d}$ (Eq. 55)

1. $\textrm{F}$ is the opposing force against the system, and $\textrm{d}$ is the distance travelled.

   1. the units for work are reported in Joules ($\textrm{J}, 1 \textrm{J} = 1 \textrm{kg} \textrm{m}^{2} \textrm{s}^{-2}$)

2. work simulates orderly motion of atoms in the surroundings.

3. there are two important things about work:

   1. if a force is being applied but no displacement results, no work is being done.

   2. if the force is perpendicular to the motion, no work is being done.

4. when work is...

   1. done on the surroundings: the capacity to do work decreases, and the internal energy of the system decreases. ($\textrm{w} \lt 0, \Delta \textrm{U} \lt 0$)

   2. done on the system: the capacity to do work increases, and the internal energy of the system increases. ($\textrm{w} \gt 0, \Delta \textrm{U} \gt 0$)

5. when a system only transfers energy as work, $\Delta \textrm{U} = \textrm{w}$.

VIII work can be classified into two types of processes:

1. expansion work: work that leads to a change in volume of the system

   1. gas expansion in a piston is a prime example of expansion work

   2. this section will mainly focus on the expansion work done by a gas in a cylinder against a piston (the opposing force)

2. nonexpansion work: work that does not involve a change in volume of the system

   1. extension of a spring, raising a weight, electrical work, etc.

VII the work done by the gas when it expands by $\Delta \textrm{V}$ against a constant external pressure $\textrm{P}_{ex}$ is:

$\textrm{w} = -\textrm{P}_{ex} \Delta \textrm{V}$ (Eq. 56)

1. when there is no external pressure on the system ($\textrm{P}_{ex} = 0$), no work is being done. This is known as free expansion.

VIII mechanical equilibrium: when the force exerted by the system is equal to the force exerted by the external pressure

1. Eq. 56 requires the external pressure to be constant throughout the expansion process

2. A system that remains in mechanical equilibrium with its surroundings at all stages of the expansion does maximum expansion work.

   1. this is also known as a reversible expansion.

IX There are two types of processes in thermodynamics:

1. reversible process: A process which can be reversed by an infinitesimal change (an extremely tiny change) in a variable

   1. when a reversible process is undone, both the system and surroundings must remain unchanged to its original state.

   2. the reversible process is an idealization and cannot happen in a real system.

2. irreversible process: A process which cannot be reversed by an infinitesimal change in a variable

X A reversible expansion is when the external pressure is continuously adjusted to match the internal pressure of the system for every stage of the expansion.

1. In other words, a system does maximum expansion work when it is in mechanical equilibrium with its surroundings at every stage of the expansion.

2. In other words, maximum expansion work is achieved in a reversible change.

XI The work done by the reversible expansion of the gas is:

$\textrm{w} = - \textrm{n}\textrm{R}\textrm{T} \textrm{ln}\frac{\textrm{V}_{f}}{\textrm{V}_{i}}$ (Eq. 57)

5.1.3 Heat

XII heat ($\textrm{q}$): energy transferred as a result of temperature difference between the system and its surroundings

1. thermal energy is the sum of kinetic energies of each individual molecule

2. temperature is the average of kinetic energy of molecules

3. the transfer of thermal energy between two bodies is heat.

   1. the body with higher thermal energy (which also has the higher temperature) will always transfer energy as heat to the body with lower thermal energy

   2. when two bodies possess the same thermal energy (and therefore the same temperature), the two bodies are in thermal equilibrium

   3. heat is just another way of transferring energy like work

   4. to put emphasis, heat is not a form of energy; it is a method of transfer

4. similar to work, if energy is solely transferred as heat, $\Delta \textrm{U} = \textrm{q}$

5. when energy is transferred as heat...

   1. to the surroundings: the thermal energy of the system decreases. This is known as an exothermic process. ($\textrm{q} \lt 0, \Delta \textrm{U} \lt 0$)

   2. to the system: the thermal energy of the system increases. This is known as an endothermic process. ($\textrm{q} \gt 0, \Delta \textrm{U} \gt 0$)

6. heat transfer stimulates random, disorderly motion of molecules in the surroundings

XIII the properties of the separation between the system and surroundings can be classified as well:

1. diathermic: walls that permits heat transfer between the system and its surroundings

2. adiabatic: walls that do not permit heat transfer between the system and its surroundings

XIV There are different types of units used for heat, other than Joules ($\textrm{J}, 1 \textrm{J} = 1 \textrm{kg} \textrm{m}^{2} \textrm{s}^{-2}$)

1. calorie (cal): the heat required to raise the temperature of 1 g of water by 1 $\degree \textrm{C}$.

   1. the modern definition is that 1 cal = 4.184 J

2. nutritional calorie (Cal): the heat requ5ired to raise the temperature of 1 kg of water by $\degree \textrm{C}$.

   1. this is equivalent to 1 kcal and is what is used for most foods.

XV heat capacity (C): the ratio of heat supplied to the change in temperature produced

$\textrm{C} = \frac{\textrm{q}}{\Delta \textrm{T}}$ (Eq. 58)

1. heat capacity is an extensive property, it is better reported as an intensive property

   1. specific heat capacity ($\textrm{C}_{s}$): the heat capacity divided by mass of body ($\frac{\textrm{C}}{\textrm{m}}$)

   2. molar heat capacity ($\textrm{C}_{m}$): the heat capacity divided by moles of body ($\frac{\textrm{C}}{\textrm{n}}$)

2. heat capacity can also differ depending on certain conditions:

   1. heat capacity at constant pressure ($\textrm{C}_{p}$)

   2. heat capacity at constant volume ($\textrm{C}_{v}$)

XVI calorimetry can be used to determine the energy transferred as heat

1. the calorimeter is commonly calibrated with a known amount of energy transferred as heat to properly interpret the change in temperature

   1. electrical heating through a known current and time allows precise calibration

   2. the amount of energy transferred as heat can be calculated by $\textrm{q}_{\textrm{cal}} = \textrm{l} \textrm{v} \Delta \textrm{t}$ (Eq.59)

   3. where I is the current, ν is the potential difference of the supply, and t is time.

2. the temperature change resulting from the calorimetry reaction can be calculated:

   1. $\textrm{q}_{\textrm{cal}} = −\textrm{q} = −\textrm{m} \textrm{C}_{s} \Delta \textrm{T} = −\textrm{n} \textrm{C}_{m} \Delta \textrm{T}$

XVII when an ideal gas goes through reversible isothermal expansion,

$\textrm{q} =\textrm{n} \textrm{R} \textrm{T} \textrm{ln}\frac{\textrm{V}_{f}}{\textrm{V}_{i}}$ (Eq. 61)