# Thermodynamics and Simple Harmonic Motion

Classified in Physics

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## Thermodynamics

### First Law of Thermodynamics (Law of Energy Conservation)

Energy cannot be created or destroyed; it can only change forms.

**Formula:** ΔU=Q−W

**Where: **ΔU is the change in internal energy of the system, Q is the heat added to the system, W is the work done by the system.

**Explanation: **The total energy in a closed system remains constant. Energy can be transformed from one form to another (e.g., heat energy to mechanical energy).

### Second Law of Thermodynamics

Key Concept: The total entropy (disorder) of an isolated system always increases or remains constant.

Formulas:

**Entropy Change for Reversible Process: ΔS=Qrev /T**

**Where: **ΔS is the change in entropy. Qrev is the heat added in a reversible process. T is the absolute temperature. Qirr is the heat added in an irreversible process.

**Entropy Change for Irreversible Process: ΔS>Qirr/ T Where: **Qirr is the heat added in an irreversible process.

**Clausius Statement: **

**ΔSuniverse≥0**

** Where: **ΔSuniverse is the change in the entropy of the universe.

**Carnot Efficiency: η=1−Tc/TH**

**Where: **η is the efficiency of a Carnot engine. TC is the absolute temperature of the cold reservoir. TH is the absolute temperature of the hot reservoir.

**Explanation: **Heat flows naturally from hot to cold objects. Entropy, a measure of disorder, tends to increase in an isolated system. Many natural processes are irreversible and increase the overall entropy.

## Simple Harmonic Motion (SHM)

Equilibrium Position: This is the position where the net force on the object is zero.

Amplitude (A): The maximum distance from the equilibrium position.

Period (T): The time it takes to complete one full cycle of motion.

Frequency (f): The number of cycles per unit of time. It is related to the period by f=1/T.

Phase (ϕ): Defines the initial state of the motion.

The position x(t) of an object in SHM as a function of time can be described by; **x(t)=Asin(ωt+φ)**

where: **A** is the amplitude. **ω** is the angular frequency, related to frequency and period by ω=2πf=2π/T.**φ** is the initial phase.

The velocity v(t) is the derivative of position with respect to time: **v(t)=dx/dt=−Aωcos(ωt+φ)**

The acceleration a(t) is the derivative of velocity with respect to time: **a(t)=dv/dt=−Aω2sen(ωt+φ)a(t) **

In SHM, the total mechanical energy remains constant and is exchanged between kinetic energy and potential energy: **Potential Energy (U):** U=1/2kx2, **Kinetic Energy (K):** K=1/2mv2, **Total Mechanical Energy (E): **E=K+U=1/2kA2. This is constant and depends only on the amplitude and the spring constant.

Simple Harmonic Motion is a type of oscillatory motion where a restoring force proportional to the displacement acts on the object. This motion is described by a sinusoidal equation involving parameters like amplitude, angular frequency, and phase. SHM is a fundamental model for understanding many types of periodic motion in physics.