Vout=Vin* R/(R+Rt)
Vin/Vout =(R+Rt)/R=1+(Rt/R) 
(Vin/Vout)-1 = Rt/R

Rt = R((Vin/Vout)-1)

Vout = ADC Reading * (5/1024)  = Vo * (5/1024)

Vin/Vout = 5/( Vo * (5/1024) = 1024/ Vo

Rt = R((Vin/Vout)-1)= R((1024/Vo)-1)

T = 1 / (A + Bln(Rt) + Cln (Rt)^3 )

#include <math.h>
#include "LiquidCrystal.h"

LiquidCrystal lcd(12,11,5,4,3,2);

float A = 1.009249522e-03, B = 2.378405444e-04, C = 2.019202697e-07;
float T,logRt,Tf,Tc;
int Vo;

void setup(){
 lcd.begin(16,2);
 lcd.clear();
}

void loop() 
{
 lcd.setCursor(0,0);
  lcd.print("Temp:");

Vo=analogRead(A0);
logRt = log(10000.0*((1024.0/Vo-1))); 
 T = (1.0 / (A + B*logRt + C*logRt*logRt*logRt));  // We get the temperature value in Kelvin from this Stein-Hart equation
 Tc = T - 273.15;                     // Convert Kelvin to Celcius
 Tf = (Tc * 1.8) + 32.0;              // Convert Kelvin to Fahrenheit

  lcd.print((T));
  lcd.print("k ");
 
 lcd.setCursor(0,1);
  lcd.print((Tc));
  lcd.print(" C ;");
 lcd.setCursor(9,1);
  lcd.print((Tf));
  lcd.print(" F");
 delay(800);
}

#include <math.h>
#include "LiquidCrystal.h"
#define RELAY 8   
LiquidCrystal lcd(12,11,5,4,3,2);
float A = 1.009249522e-03, B = 2.378405444e-04, C = 2.019202697e-07;
float T,logRt,Tc;
int Vo;

void setup() {
 lcd.begin(16,2);
 lcd.clear();
pinMode(RELAY, OUTPUT); 
}

void loop() {
  lcd.setCursor(0,0);
  lcd.print("Temperature:");

Vo=analogRead(A0);
logRt = log(10000.0*((1024.0/Vo-1))); 
 T = (1.0 / (A + B*logRt + C*logRt*logRt*logRt));  // We get the temperature value in Kelvin from this Stein-Hart equation
 Tc = T - 273.15;                 // Convert Kelvin to Celcius

  lcd.print(int(Tc));
  lcd.print("C ");
  delay(500);  // wait 0.5 seconds before sampling temperature again

if (Tc < 28) 
{
digitalWrite(RELAY, HIGH);
lcd.setCursor(0,1);
lcd.print("Heater status:ON ");
delay(500);
}

else if (Tc > 28) 
{
digitalWrite(RELAY, LOW);
lcd.setCursor(0,1);
lcd.print("Heater status:OFF");
delay(500);
}   
         
}

Duty Cycle =Turn ON time/ (Turn ON time + Turn OFF time)

Frequency = 1/Time Period
Time Period = On time + Off time

Output Voltage = Duty cycle (%) * 5

analogWrite(0)

analogWrite(127)

analogWrite(255)

analogWrite(pin, value)

const int LED = 9; // the pin for the LED
int i = 0; // We'll use this to count up and down
void setup() 
{
pinMode(LED, OUTPUT); // tell Arduino LED is an output
}

void loop()
{
for (i = 0; i < 255; i++) 
{ // loop from 0 to 254 (fade in)
analogWrite(LED, i); // set the LED brightness
delay(10); // Wait 10ms because analogWrite
// is instantaneous and we would  not see any change
}
for (i = 255; i > 0; i--) 
{ // loop from 255 to 1 (fade out)
analogWrite(LED, i); // set the LED brightness
delay(10); // Wait 10ms
}
}

/*
  Fading

  This example shows how to fade an LED using the analogWrite() function.

  The circuit:
  - LED attached from digital pin 9 to ground.

*/

int ledPin = 9;    // LED connected to digital pin 9

void setup() {
  // nothing happens in setup
}

void loop() {
  // fade in from min to max in increments of 5 points:
  for (int fadeValue = 0 ; fadeValue <= 255; fadeValue += 5) {
    // sets the value (range from 0 to 255):
    analogWrite(ledPin, fadeValue);
    // wait for 30 milliseconds to see the dimming effect
    delay(30);
  }

  // fade out from max to min in increments of 5 points:
  for (int fadeValue = 255 ; fadeValue >= 0; fadeValue -= 5) {
    // sets the value (range from 0 to 255):
    analogWrite(ledPin, fadeValue);
    // wait for 30 milliseconds to see the dimming effect
    delay(30);
  }
}

int ledPin = 9;      // LED connected to digital pin 9
int analogPin = 3;   // potentiometer connected to analog pin 3
int val = 0;         // variable to store the read value

void setup() {
  pinMode(ledPin, OUTPUT);  // sets the pin as output
}

void loop() {
  val = analogRead(analogPin);  // read the input pin
  analogWrite(ledPin, val / 4); // analogRead values go from 0 to 1023, analogWrite values from 0 to 255
}

 pinMode(ledPin, OUTPUT);
analogWrite(pin, value);

int i=0;//initializing a integer for incrementing and decrementing duty ratio.
void setup()
{
     pinMode(3, OUTPUT);   // sets the pin3 as output
     pinMode(0, INPUT);// sets the pin0 as input
     pinMode(1, INPUT);// sets the pin1 as input 
}
 
void loop()
{
     analogWrite(3, i);  // analogWrite values from 0 to 255
      if (digitalRead(0)==LOW)
      {
          if (i<255)
         {
           i++;//if pin0 is pressed and the duty ratio value is less than 255
           delay(30);
          }
       }  
               
      if (digitalRead(1)==LOW)
     {
        if (i>0)
        {
          i--;// if pin1 is pressed and the duty ratio value is greater than 0
          delay(30);
         }
    }
}

void setup()
{
   for (int i=0;i<8;i++)
   {
     pinMode(i, INPUT_PULLUP);//take pins0-7 as inputs with default high or pulled up pins.
   }
   pinMode(9,OUTPUT);//buzzer output at pin9
}
 
// the loop routine runs over and over again forever:
void loop()
{

  if (digitalRead(0)==LOW)
  {
     analogWrite(9,25);//if button 1 is pressed PWM of duty ratio(25*100)/255 is given to buzzer
     delay(100);
     analogWrite(9,0);
  }

 if (digitalRead(1)==LOW)
 {
   analogWrite(9,50); //if button 2 is pressed PWM of duty ratio(50*100)/255 is given to buzzer
 
     delay(100);
     analogWrite(9,0);
}
if (digitalRead(2)==LOW)
{
   analogWrite(9,75);// /if button 3 is pressed PWM of duty ratio(75*100)/255 is given to buzzer       delay(100);
   analogWrite(9,0);
 }
if (digitalRead(3)==LOW)
{
  analogWrite(9,100); //if button 4 is pressed PWM of duty ratio(100*100)/255 is given to buzzer
 delay(100);
 analogWrite(9,0);
 }
if (digitalRead(4)==LOW)
{
 analogWrite(9,125);
 delay(100);
 analogWrite(9,0);
}
if (digitalRead(5)==LOW)
{
  analogWrite(9,150);
  delay(100);
   analogWrite(9,0);
 }
if (digitalRead(6)==LOW)
{
 analogWrite(9,175);
 delay(100);
 analogWrite(9,0);
 }
 if (digitalRead(7)==LOW)
{
  analogWrite(9,200);
  delay(100);
  analogWrite(9,0);
 }
}