What is the fundamental principle behind the First Law of Thermodynamics?

The First Law of Thermodynamics is fundamentally a statement of the conservation of energy. It asserts that energy can neither be created nor destroyed within an isolated system. Instead, it can only be transformed from one form to another, such as from heat to work, or stored as internal energy. This means that the total energy of the universe remains constant, and any change in a system's energy must be accounted for by energy transfer across its boundaries in the form of heat or work.

How do I correctly apply the sign conventions for heat and work in the First Law equation?

Sign conventions are crucial. For the equation $\Delta U = Q - W$: $Q$ is positive when heat is *added to* the system and negative when heat is *removed from* the system. $W$ is positive when work is done *by* the system (e.g., expansion) and negative when work is done *on* the system (e.g., compression). Always define your system clearly and stick to these conventions to avoid errors in calculations.

Can internal energy change in an isothermal process?

For an *ideal gas*, internal energy depends solely on its temperature. Therefore, in an isothermal process (constant temperature), the change in internal energy ($\Delta U$) for an ideal gas is zero. However, for *real gases* or other systems (like phase changes), internal energy can change even at constant temperature due to changes in intermolecular potential energy. For NEET, assume ideal gas behavior unless specified otherwise.

What is the significance of Mayer's relation, $C_P - C_V = R$?

Mayer's relation, $C_P - C_V = R$, is a fundamental relationship for ideal gases that connects the molar specific heat capacity at constant pressure ($C_P$) and constant volume ($C_V$) with the universal gas constant ($R$). It signifies that $C_P$ is always greater than $C_V$ because, at constant pressure, some of the heat supplied is used to do work against the surroundings (expansion), in addition to increasing the internal energy. At constant volume, all the heat supplied goes directly into increasing internal energy.

How does the First Law relate to P-V diagrams?

P-V diagrams are powerful tools for visualizing thermodynamic processes. The work done by a system during a process is represented by the area under the curve on a P-V diagram. For an expansion, the area is positive (work done by the system); for compression, it's negative (work done on the system). For a cyclic process, the net work done is the area enclosed by the loop. The First Law then helps relate this work to the net heat exchange and internal energy change over the cycle.

First Law of Thermodynamics

Physics

NEET UG

Version 1Updated 23 Mar 2026

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The First Law of Thermodynamics is a fundamental principle in physics, essentially a restatement of the law of conservation of energy applied to thermodynamic systems. It posits that energy cannot be created or destroyed in an isolated system, only transformed from one form to another. Specifically, for a thermodynamic system, the change in its internal energy ( $Delta U$ ) is equal to the heat ( $Q$ …

Quick Summary

The First Law of Thermodynamics is a direct application of the principle of conservation of energy to thermodynamic systems. It states that the change in a system's internal energy ( $Delta U$ ) is equal to the heat ( $Q$ ) added to the system minus the work ( $W$ ) done *by* the system on its surroundings, expressed as $Delta U = Q - W$ .

Internal energy ( $U$ ) is a state function, depending only on the system's current state (primarily temperature for ideal gases). Heat ( $Q$ ) and work ( $W$ ) are path functions, representing energy transfer mechanisms.

Crucial sign conventions dictate that $Q$ is positive for heat absorbed and negative for heat released, while $W$ is positive for work done by the system (expansion) and negative for work done on the system (compression).

This law helps analyze various thermodynamic processes: isochoric ( $Delta U = Q_V$ , $W=0$ ), isobaric ( $Q_P = Delta U + PDelta V$ ), isothermal ( $Delta U = 0$ , $Q=W$ for ideal gases), and adiabatic ( $Delta U = -W$ , $Q=0$ ).

Mayer's relation, $C_P - C_V = R$ , links specific heats for ideal gases. The First Law is fundamental to understanding energy conversion in engines, refrigerators, and all physical and biological systems.

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Key Concepts

Internal Energy (

Delta U

) and Temperature

For an ideal gas, internal energy is directly proportional to its absolute temperature. This is because the…

Work Done in P-V Processes

Work done by a gas during expansion or compression is given by $W = \int P dV$ . On a P-V diagram, this…

Mayer's Relation and Ratio of Specific Heats

Mayer's relation, $C_P - C_V = R$ , is a crucial link between the molar specific heat capacities at constant…

First Law —

\Delta U = Q - W

(where

W

is work done *by* system).

Sign Conventions —

Q > 0

(absorbed),

Q < 0

(released);

W > 0

(by system),

W < 0

(on system).

Internal Energy (Ideal Gas) —

U \propto T

, so

\Delta U = 0

for isothermal processes.

\Delta U = nC_V\Delta T

for any process.

Work Done — Area under P-V curve.

W_{isobaric} = P\Delta V

W_{isothermal} = nRT \ln(V_f/V_i)

Isochoric —

W=0 \implies \Delta U = Q_V

Isobaric —

W=P\Delta V \implies Q_P = \Delta U + P\Delta V

Isothermal (Ideal Gas) —

\Delta U=0 \implies Q=W

Adiabatic —

Q=0 \implies \Delta U = -W

. Also

PV^\gamma = \text{constant}

TV^{\gamma-1} = \text{constant}

Cyclic Process —

\Delta U=0 \implies Q=W_{net}

Mayer's Relation —

C_P - C_V = R

Ratio of Specific Heats —

\gamma = C_P/C_V

. Monatomic:

\gamma = 5/3

. Diatomic:

\gamma = 7/5

Quickly Understand Work: Q is for Quantity of heat, U is for Unique internal energy, W is for Work done. Remember the equation $\Delta U = Q - W$ . Think of it as: 'Energy Update equals Quick heat in, minus Work out.' For signs: 'Heat IN is INcrease (positive Q), Work OUT is OUTput (positive W).'