Find the change in enthalpy of oxygen gas as it is heated

Question

Problem 1 - Consider the following data from a three-stage mode rocket launch:

Time (seconds)	Altitude (meters)
0	0
1.00	107.37
2.00	210.00
3.00	307.63
4.00	400.00
5.00	484.60
6.00	550.00
7.00	583.97
8.00	580.00
9.00	549.53
10.00	570.00
11.00	699.18
12.00	850.00
13.00	927.51
14.00	950.00
15.00	954.51
16.00	940.00
17.00	910.68
18.00	930.00
19.00	1041.52
20.00	1150.00
21.00	1158.24
22.00	1100.00
23.00	1041.76
24.00	1050.00

Use the subplot command to the following sections to plot on the same graphing window.

(a) Create a plot with time on the x-axis and altitude on the y-axis.

(b) Use the diff function to determine the velocity during each time interval, and plot the velocity against the starting time for each interval.

(c) Use the diff function again to determine the acceleration for each time interval, and plot the acceleration against the starting time for each interval.

Problem 2 - The equation, C_p = a + bT + cT² + dT³ is an empirical polynomial that describes the behavior of the heat capacity C_p as a function of temperature in Kelvin. The change is enthalpy (a measure of energy) as a gas is heated from T₁ to T₂ is the integral of this equation with respect to T:

Δh = _{T_1}∫^T_2 C_pdT

Find the change in enthalpy of oxygen gas as it is heated from 300K to 1000K, using the integral function. The values of a, b, c, and d for oxygen are as follows:

a = 25.48

b = 1.52 × 10^-2

c = -0.7155 × 10^-5

d = 1.312 × 10^-9

Problem 3 - Solve the following differential equation for values of t between 0 and 4, with the initial condition of y = 1 when t = 0,

dy/dt + sin(t) = 1

(a) Solve the above equation analytically using MATLAH's symbolic capabilities.

(b) Solve using the ode45 function.

(c) Plot your results for both approaches on the same graph.