Computer Applications in Chemical Engineering
Using MathCad to do Integration, Summation, etc.
In Chemical Engineering it is frequently necessary to find the area under a curve (compute an integral) either
numerically or analytically. MathCad makes this easy by having both symbolic and numerical integration and
summation functions.
The Thermodynamic definition of the heat capacity is:
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑄 𝑑𝑄
=
= 𝐶𝑝
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑇 𝑑𝑇
When integrated (the area under the curve is found), this equation gives the amount of heat “Q” required to raise
the temperature of a unit mass of a pure substance from one temperature to another, assuming no phase change.
The heat capacity of liquid water is reported to be:
Cp(T)=a+bT+cT2+dT3 (kJ/mole-K)
where a=33.46103, b=0.6880×10-5, c=0.7604×10-8, d=-3.593×10-12.
1.
2.
3.
Use symbolic integration to compute the amount of heat required to raise one mole of liquid water from
22 oC to 91 oC.
Do the same calculation numerically.
Do the same calculation using a summation. Illustrate how your choice of integration step size affects the
results as compared to the analytical solution.
In thermodynamics, the work done on a system is defined as:
𝑉2
𝑊 = − ∫ 𝑃𝑑𝑉
𝑉1
where, P is the pressure as a function of volume, V is the volume and V1 and V2 are the initial and final volumes in
a system.
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7.
Find the amount of work required to compress one mole of steam (water vapor) at a constant
temperature of 600 K from a volume of 100 L to 50 L (L=liters). Do this calculation using the built in
numerical integration function using both the “Adaptive” and “Romberg” integration.
Use the trapezoidal rule and a summation also to estimate the work. Comment on the effect that
integration step size has on accuracy.
Attempt to do the integration analytically. Comment if you cannot make this work
Explain why your choice of step size has very little affect when you integrate Cp(T), but has more affect
when you integrate P(V). HINT: Consider plotting Cp(T) vs T and compare it to P(V) vs V.