Class 12 > Unit # 16:First Law of Thermodynamics > First Law Of Thermodynamics & Applications

Class 11 Physics • Thermodynamics

First Law of Thermodynamics & Its Applications

Statement, mathematical formulation, sign conventions, and step-by-step application to Isobaric, Isochoric, Isothermal, and Adiabatic processes.

1. Statement & Mathematical Form

Statement: Whenever heat energy is converted into another type of energy, or when another form of energy is converted into heat energy, the total amount of energy remains constant. In other words, the First Law of Thermodynamics is simply a statement of the Law of Conservation of Energy.

Alternative Definition: When heat energy ($\Delta Q$) is supplied to a system, it is utilized in two parts: to change the internal energy of the system ($\Delta U$) and to perform external work by the system ($\Delta W$).

$$\Delta Q = \Delta U + \Delta W$$

Or since work done at constant pressure is $\Delta W = P \Delta V$: $$\Delta Q = \Delta U + P \Delta V$$

Sign Conventions

• $\Delta Q$ is Positive ($+$): When heat is supplied to the system.
• $\Delta Q$ is Negative ($-$): When heat is rejected by the system.
• $\Delta W$ is Positive ($+$): When work is done by the system (Expansion).
• $\Delta W$ is Negative ($-$): When work is done on the system (Compression).
• $\Delta U$ is Positive ($+$): When temperature/internal energy increases.
• $\Delta U$ is Negative ($-$): When temperature/internal energy decreases.

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2. Four Applications of the First Law

1. Isobaric Process ($P = \text{Constant}$)

A thermodynamic process in which external pressure remains constant.

Supplied heat energy increases internal energy and performs work to move the piston:

$$\Delta W = F \cdot \Delta x = (P A) \cdot \Delta x = P \Delta V$$

Substituting into the First Law gives:

$$\Delta Q_p = \Delta U + P \Delta V$$

Outcome: Heat supplied at constant pressure equals the change in total enthalpy of the system.

2. Isochoric Process ($V = \text{Constant}$)

A thermodynamic process in which the volume of the system remains fixed.

Since the piston remains fixed, there is no change in volume ($\Delta V = 0$):

$$\Delta W = P \Delta V = P(0) = 0$$

Substituting into the First Law gives:

$$\Delta Q_v = \Delta U$$

Outcome: All heat supplied goes directly toward increasing the internal energy (and temperature) of the system.

3. Isothermal Process ($T = \text{Constant}$)

A thermodynamic process conducted at constant temperature (Boyle's Law holds valid: $P \propto 1/V$).

Since internal energy depends solely on temperature for an ideal gas, $\Delta T = 0$ implies $\Delta U = 0$:

$$\Delta Q = 0 + \Delta W$$ $$\Delta Q = \Delta W$$

Outcome: All heat supplied to the system is entirely converted into external mechanical work.

4. Adiabatic Process ($\Delta Q = 0$)

A process in which no heat enters or leaves the system ($\Delta Q = 0$). Temperature does not remain constant.

Substituting $\Delta Q = 0$ into the First Law gives:

$$0 = \Delta U + \Delta W$$ $$\Delta W = -\Delta U \quad \text{or} \quad \Delta U = -\Delta W$$

Outcome: Work done by the gas during expansion comes at the expense of its own internal energy, causing cooling.

Summary of First Law Transformations:

• Isobaric: $\Delta Q = \Delta U + P\Delta V$
• Isochoric: $\Delta Q = \Delta U$
• Isothermal: $\Delta Q = \Delta W$
• Adiabatic: $\Delta W = -\Delta U$