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Gas Law Symbolic Equation

asked 2012-08-30 07:42:36 -0500

anonymous user


Ideal Gas Law[Relates Pressure and Volume]

Definitions v3

#Main Tank Pressure[Pascals]
#Tank Volume[m^3]
#Moles of Air
#n= 0
#Gas Constant
#Ambient Temperature[Kelvin][70F]
t= 294.261
eng5= [solve(Pp*Vt == n*r*t,n) for Pp in np.arange(103421.359,1013529,6895.75729)]

Why does this say:

TypeError: The first argument must be a symbolic expression or a list of
symbolic expressions.

I have the variables defined elsewhere[Pp =var('Pp')] but I'm not sure why this won't work. Thanks

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answered 2012-08-30 08:05:42 -0500

DSM gravatar image

updated 2012-08-30 08:07:13 -0500

The first step in debugging is to look to see what the first argument actually is. I'm assuming that you did n = var("n") or something at some point. So we can get the first element:

sage: Pps = np.arange(103421.359,1013529,6895.75729) 
sage: Pps[0]
sage: Pp = Pps[0]
sage: Pp * Vt
sage: Pp * Vt == n
sage: Pp * Vt == n*r*t

.. and we see that Sage is automatically evaluating the expression, and since it can't prove that it's true -- which is good, because it's not true in general -- it's saying that it's False.

Ultimately this is because

sage: type(Pp)
<type 'numpy.float64'>

Pp is a numpy float, which doesn't interact too well with the Sage types. As soon as the __eq__ method of the float is called, the game's over. You can work around this in some fragile ways, such as flipping the order:

sage: n*r*t == Pp*Vt  
2446.62193200810*n == 144.055610951
sage: solve(n*r*t == Pp*Vt, n)
[n == (52361895020038/889307677165161)]

But a better and more robust way would be to avoid getting numpy involved at all, and stick with Sage-native objects. For example, you can use srange and sxrange:

srange(start, end=None, step=1, universe=None, check=True, include_endpoint=False, endpoint_tolerance=1e-05)
    Return list of numbers ``a, a+step, ..., a+k*step``,
    where ``a+k*step < b`` and ``a+(k+1)*step >= b`` over
    exact rings, and makes a best attempt for inexact rings 
    (see note below).

which would give:

sage: s = srange(103421.359,1013529,6895.75729)
sage: len(s)
sage: s[:5]
[103421.359000000, 110317.116290000, 117212.873580000, 124108.630870000, 131004.388160000]

and then

sage: eng5= [solve(Pp*Vt == n*r*t,n) for Pp in srange(103421.359,1013529,6895.75729)]
sage: len(eng5)
sage: eng5[:3]
[[n == (52361895020038/889307677165161)], [n == (56778965120683/904048017111831)], [n == (74168281138961/1111449736506101)]]

Short version: don't use numpy unless you need to, and here you don't.

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Could you elaborate on when one might use srange, xrange or np.arange? Why did someone request using np.arange on this problem: I see that srange() works there, but xrange() does not. Is it because srange and np.arange both generate a list output, but xrange does it dynamically? Thanks for the clarification!

duke11235 gravatar imageduke11235 ( 2012-08-30 08:33:26 -0500 )edit

`xrange` is a Python lazy range (the "x" means "lazy" for historical reasons), and yields Python `int`s. They don't have a lot of the Sage special methods, and dividing `int(5)` by `int(2)` gives 2 (truncating division) rather than the fraction 5/2. You also can't use it with floats. `srange` -- the "S" stands for "Sage" -- handles lots of different kinds of Sage objects. See also the ` [1, 1.5, .., 10]` syntax. `np.arange` is seldom useful in Sage, but is really useful in standard Python, because Python doesn't have a builtin "range" that works with non-integers. Does that make sense?

DSM gravatar imageDSM ( 2012-08-30 08:51:56 -0500 )edit

Thanks. That clears it right up.

duke11235 gravatar imageduke11235 ( 2012-08-30 10:12:25 -0500 )edit

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Asked: 2012-08-30 07:42:36 -0500

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Last updated: Aug 30 '12