Least square method for chemical engineering Problem by hand calculation Part -1 скачать в хорошем качестве

Least square method for chemical engineering Problem by hand calculation Part -1

Least square method for chemical engineering Problem by hand calculation Part -1 T = -40 0 40 80 120 160 %deg C T = 233 273 313 353 393 433 P = 6900 8100 9350 10500 11700 12800 Employ the ideal gas law pV = nRT to determine R on the basis of these data. Note that for the law, T must be expressed in kelvins. a) Calculate R from the linear fit by a Least square technique in MATLAB and Excel and Plot T vs P b) Calculate R from poly fit and Plot T vs P c) finally, calculate P at temperature T = 100 (°C) The Least Squares Method is a mathematical technique commonly used in chemical engineering for approximating the parameters of a model that minimizes the sum of the squared differences between observed and predicted values. By hand calculation, this method involves finding the coefficients of a model equation that best fits a set of experimental data points. Here's a step-by-step description of applying the Least Squares Method for a chemical engineering problem by hand calculation: Define the Model Equation: Start with a proposed model equation that represents the relationship between the independent and dependent variables. For example, it could be a linear equation like y=mx+b or a more complex equation depending on the nature of the problem. Collect Experimental Data: Gather experimental data pairs (x i ,y i ) relevant to the problem. These data points represent the observed values of the dependent variable (y) corresponding to different values of the independent variable (x). Differentiate the objective function with respect to the model parameters and set the derivatives to zero. Solve the resulting system of equations to find the values of the parameters that minimize the objective function. This may involve algebraic manipulation or calculus depending on the complexity of the model. Calculate Model Parameters: Use the solved parameters to obtain the final model equation that best fits the experimental data. Evaluate Model Performance: Validate the model by comparing the predicted values with the observed values. Calculate residuals and assess the goodness of fit through statistical measures like the coefficient of determination (R-squared). Iterate if Necessary: If the model does not adequately fit the data, consider refining the model equation or exploring more complex models. Iterate the process until a satisfactory fit is achieved. By performing these steps by hand, engineers gain a deep understanding of the underlying principles of the Least Squares Method and its application to chemical engineering problems. It also provides insights into the accuracy and reliability of the model for making predictions based on experimental data.