Simulation of Newton’s Law of Cooling Gaming Project in C++

#include <iostream>
#include <cmath>
#include <iomanip>

class NewtonsLawOfCoolingSimulator {
private:
    double initialTemperature; // Initial temperature of the object
    double ambientTemperature; // Ambient temperature
    double coolingConstant;    // Cooling constant (k)
    double timeStep;           // Time step for the simulation

public:
    // Constructor
    NewtonsLawOfCoolingSimulator(double initialTemperature, double ambientTemperature, double coolingConstant, double timeStep)
        : initialTemperature(initialTemperature), ambientTemperature(ambientTemperature), coolingConstant(coolingConstant), timeStep(timeStep) {}

    // Function to simulate cooling over time
    void simulate(double totalTime) const {
        int steps = static_cast<int>(totalTime / timeStep);
        double currentTemperature = initialTemperature;

        std::cout << "Time\tTemperature\n";
        std::cout << "-----------------------\n";

        for (int i = 0; i <= steps; ++i) {
            double time = i * timeStep;
            currentTemperature = ambientTemperature + (initialTemperature - ambientTemperature) * exp(-coolingConstant * time);
            std::cout << std::fixed << std::setprecision(2) << time << "\t" << currentTemperature << "\n";
        }
    }
};

int main() {
    double initialTemperature, ambientTemperature, coolingConstant, timeStep, totalTime;

    // Input parameters from the user
    std::cout << "Enter the initial temperature of the object: ";
    std::cin >> initialTemperature;
    std::cout << "Enter the ambient temperature: ";
    std::cin >> ambientTemperature;
    std::cout << "Enter the cooling constant (k): ";
    std::cin >> coolingConstant;
    std::cout << "Enter the time step for the simulation: ";
    std::cin >> timeStep;
    std::cout << "Enter the total time for the simulation: ";
    std::cin >> totalTime;

    // Create a NewtonsLawOfCoolingSimulator object
    NewtonsLawOfCoolingSimulator simulator(initialTemperature, ambientTemperature, coolingConstant, timeStep);

    // Run the simulation
    simulator.simulate(totalTime);

    return 0;
}

#include <iostream>

#include <cmath>

#include <iomanip>

class NewtonsLawOfCoolingSimulator {

private:

double initialTemperature; // Initial temperature of the object

double ambientTemperature; // Ambient temperature

double coolingConstant; // Cooling constant (k)

double timeStep; // Time step for the simulation

public:

// Constructor

NewtonsLawOfCoolingSimulator(double initialTemperature, double ambientTemperature, double coolingConstant, double timeStep)

: initialTemperature(initialTemperature), ambientTemperature(ambientTemperature), coolingConstant(coolingConstant), timeStep(timeStep) {}

// Function to simulate cooling over time

void simulate(double totalTime) const {

int steps = static_cast<int>(totalTime / timeStep);

double currentTemperature = initialTemperature;

std::cout << "Time\tTemperature\n";

std::cout << "-----------------------\n";

for (int i = 0; i <= steps; ++i) {

double time = i * timeStep;

currentTemperature = ambientTemperature + (initialTemperature - ambientTemperature) * exp(-coolingConstant * time);

std::cout << std::fixed << std::setprecision(2) << time << "\t" << currentTemperature << "\n";

}

};

int main() {

double initialTemperature, ambientTemperature, coolingConstant, timeStep, totalTime;

// Input parameters from the user

std::cout << "Enter the initial temperature of the object: ";

std::cin >> initialTemperature;

std::cout << "Enter the ambient temperature: ";

std::cin >> ambientTemperature;

std::cout << "Enter the cooling constant (k): ";

std::cin >> coolingConstant;

std::cout << "Enter the time step for the simulation: ";

std::cin >> timeStep;

std::cout << "Enter the total time for the simulation: ";

std::cin >> totalTime;

// Create a NewtonsLawOfCoolingSimulator object

NewtonsLawOfCoolingSimulator simulator(initialTemperature, ambientTemperature, coolingConstant, timeStep);

// Run the simulation

simulator.simulate(totalTime);

return 0;

}

Explanation

Class Definition (NewtonsLawOfCoolingSimulator):
- Private Members:
  - initialTemperature: Initial temperature of the object.
  - ambientTemperature: Temperature of the surrounding environment.
  - coolingConstant: Cooling constant (k), which determines the rate of cooling.
  - timeStep: Interval of time between calculations in the simulation.
Constructor:
- Initializes the simulation parameters with the provided values.
simulate Method:
- Computes and prints the temperature of the object over time.
- Uses the formula $T_a + (T_0 – T_a) \cdot e^{-kt}$ , where $T (t)$ is the temperature at time $t$ , $T_0$ is the initial temperature, $T_a$ is the ambient temperature, and $k$ is the cooling constant.
- Iterates through each time step, updating and displaying the object’s temperature.
main Function:
- Prompts the user to input values for the initial temperature, ambient temperature, cooling constant, time step, and total time.
- Creates an instance of NewtonsLawOfCoolingSimulator with the user’s parameters.
- Calls the simulate method to output the temperature simulation results over the specified total time.

Simulation of Newton’s Law of Cooling Gaming Project in C++

Explanation

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