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# write a program in MATLAB in a single script for the following 2 cases

INSTRUCTIONS TO CANDIDATES
###### ANSWER ALL QUESTIONS

Programming Problem

Your task is to write a program in MATLAB in a single script for the following 2 cases:

Case 1: Ideal gas v/s real gas

The Van der Waals equation (Equation 1) gives a relationship between the pressure P (atm), volume V (L), and temperature T (K) for a real gas.

P=nRT/(V-b)-  (n^2 a)/V^2

(1)

where R is the gas constant and has a value of 0.08206 (L atm)/(mol K).  a and b are material constants for nitrogen with values of 1.39 L2 atm/mol2 and 0.03913 l/mol. n is the number of moles. Make a 3-D surface plot that shows the variation of the pressure (dependent variable, z axis) with respect to both the volume (independent variable, x axis) and temperature (independent variable, y axis) for nitrogen gas. The range for the volume V and temperature T are as follows: 1.0 ≤V ≤3.0 L and 273 ≤T ≤473 K. Take n as 2.5 moles.

Important: In your group presentation, you should also describe the difference between a real gas is from an ideal gas. What assumptions are made for an ideal gas. What equation of state can be used for an ideal gas? Are there other real gas equations? Please reference your findings.

Case 2: Flight of a model rocket

The flight of a model rocket can be modelled as follows. During the first 0.50s the rocket is propelled upward by the rocket engine with a force of 32 N. The rocket then flies up while slowing down under the force of gravity. After it reaches the apex, the rocket starts to fall back down. When its downward velocity reaches 10 m/s, a parachute opens (assumed to open instantly).

For simplicity, it is assumed that the mass of the rocket is constant at all times during the flight.

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