What is the primary statement of the First Law of Thermodynamics?

The primary statement of the First Law of Thermodynamics is the principle of conservation of energy. It asserts that energy can neither be created nor destroyed, but can only be transformed from one form to another. For a thermodynamic system, this translates to the mathematical expression $Delta U = q + w$, where $Delta U$ is the change in internal energy, $q$ is the heat exchanged, and $w$ is the work done. This means the total energy of an isolated system remains constant.

What is the difference between internal energy, heat, and work?

Internal energy ($U$) is a state function, representing the total energy contained within a system (kinetic and potential energy of molecules). Its change ($Delta U$) depends only on the initial and final states. Heat ($q$) and work ($w$) are path functions, meaning their values depend on the specific process or path taken. Heat is energy transfer due to temperature difference, while work is energy transfer not due to temperature difference (e.g., mechanical work like expansion/compression). Both $q$ and $w$ are ways energy is transferred into or out of a system, contributing to the change in its internal energy.

Why is internal energy considered a state function, but heat and work are not?

Internal energy is a state function because its value is determined solely by the current state variables of the system (like temperature, pressure, volume). Regardless of how the system reached that state, its internal energy will be the same. Heat and work, however, are path functions because the amount of heat exchanged or work done depends entirely on the specific process or 'path' followed between the initial and final states. Different paths between the same two states will generally involve different amounts of heat and work, even if the change in internal energy is the same.

What are the sign conventions for heat and work in the First Law equation?

The IUPAC sign conventions, commonly used in chemistry, are crucial for applying the First Law correctly. Heat ($q$) is positive when absorbed by the system (endothermic) and negative when released by the system (exothermic). Work ($w$) is positive when done *on* the system by the surroundings (e.g., compression) and negative when done *by* the system on the surroundings (e.g., expansion). This convention ensures consistency in the $Delta U = q + w$ equation.

How does the First Law apply to an adiabatic process?

An adiabatic process is characterized by no heat exchange between the system and its surroundings, meaning $q=0$. In this scenario, the First Law simplifies to $Delta U = w_{ad}$. This implies that any change in the internal energy of the system is solely due to the work done on or by the system. If the system does work (expansion), its internal energy decreases, leading to a drop in temperature. If work is done on the system (compression), its internal energy increases, causing a rise in temperature.

What is the significance of enthalpy ($Delta H$) in relation to the First Law?

Enthalpy ($H$) is a thermodynamic property defined as $H = U + PV$. Its change, $Delta H$, is particularly significant for processes occurring at constant pressure, which are very common in chemistry (e.g., reactions in open beakers). Under constant pressure conditions, the heat exchanged ($q_p$) is equal to the change in enthalpy ($Delta H = q_p$). This makes enthalpy a convenient measure for tracking heat changes in isobaric processes, as it directly relates to the heat absorbed or released by the system without needing to account for PV work separately.

First Law of Thermodynamics

Chemistry

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The First Law of Thermodynamics, also known as the Law of Conservation of Energy, states that energy cannot be created or destroyed in an isolated system. It can only be transformed from one form to another. In the context of a thermodynamic system, this law is expressed as the change in the internal energy of a system ( $Delta U$ ) being equal to the heat ( $q$ ) added to the system plus the work ($w…

Quick Summary

The First Law of Thermodynamics is fundamentally the law of conservation of energy applied to thermodynamic systems. It states that energy cannot be created or destroyed, only transformed. Mathematically, it's expressed as $Delta U = q + w$ , where $Delta U$ is the change in the system's internal energy, $q$ is the heat exchanged, and $w$ is the work done.

Internal energy ( $U$ ) is a state function, depending only on the system's current state. Heat ( $q$ ) and work ( $w$ ) are path functions, depending on the process. Key sign conventions: $q > 0$ for heat absorbed, $q < 0$ for heat released; $w > 0$ for work done *on* the system, $w < 0$ for work done *by* the system.

Different thermodynamic processes (isochoric, isobaric, isothermal, adiabatic, cyclic) lead to specific simplifications of the First Law, allowing for calculations of energy changes. Enthalpy ( $Delta H = q_p$ ) is a crucial concept derived from the First Law for constant pressure processes.

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First Law —

\Delta U = q + w

(Conservation of Energy)

Internal Energy ($U$) — State function. For ideal gas,

U = f(T)

only.

\Delta U = nC_v\Delta T

Heat ($q$) — Path function.

+q

(absorbed),

-q

(released).

Work ($w$) — Path function.

+w

(on system),

-w

(by system).

PV Work —

w = -P_{ext}\Delta V

Reversible Isothermal Work (Ideal Gas) —

w = -nRT \ln(V_2/V_1) = -nRT \ln(P_1/P_2)

Isochoric Process ($\Delta V = 0$) —

w = 0 \implies \Delta U = q_v

Isobaric Process ($P = ext{constant}$) —

w = -P\Delta V \implies \Delta H = q_p

. Enthalpy

H = U + PV

Isothermal Process ($\Delta T = 0$) — For ideal gas,

\Delta U = 0 \implies q = -w

Adiabatic Process ($q = 0$) —

\Delta U = w_{ad}

Cyclic Process —

\Delta U = 0 \implies q_{cycle} = -w_{cycle}

Mayer's Relation (Ideal Gas) —

C_p - C_v = R

Conversion —

1,\text{L atm} = 101.3,\text{J}

To remember the First Law and its signs: 'Q-W-U'

Queer Work Understood:

\Delta U = q + w

Queer (Heat): Quickly Increases (positive for absorbed), Out (negative for released).

Work: When On (positive for on system), By (negative for by system).

For processes: 'I-A-I-A-C' (Isothermal, Adiabatic, Isochoric, Isobaric, Cyclic)

Isothermal: Temperature Constant (

\Delta T=0 \implies \Delta U=0 \implies q=-w

for ideal gas).

Adiabatic: Quiet (No heat,

q=0 \implies \Delta U=w

Isochoric: Volume Constant (

\Delta V=0 \implies w=0 \implies \Delta U=q_v

Isobaric: Pressure Constant (

\Delta H=q_p

Cyclic: U-turn (Back to start,

\Delta U=0 \implies q=-w