def bubble_at_T(zs, Psats, fugacities=None, gammas=None):
    '''
    >>> bubble_at_T([0.5, 0.5], [1400, 7000])
    4200.0
    >>> bubble_at_T([0.5, 0.5], [1400, 7000], gammas=[1.1, .75])
    3395.0
    >>> bubble_at_T([0.5, 0.5], [1400, 7000], gammas=[1.1, .75], fugacities=[.995, 0.98])
    3452.440775305097
    '''
    if not fugacities:
        fugacities = [1 for i in range(len(Psats))]
    if not gammas:
        gammas = [1 for i in range(len(Psats))]
    if not none_and_length_check((zs, Psats, fugacities, gammas)):
        raise Exception('Input dimentions are inconsistent or some input parameters are missing.')
    P = sum(zs[i]*Psats[i]*gammas[i]/fugacities[i] for i in range(len(zs)))
    return P
def bubble_at_T(zs, Psats, fugacities=None, gammas=None):
    '''
    >>> bubble_at_T([0.5, 0.5], [1400, 7000])
    4200.0
    >>> bubble_at_T([0.5, 0.5], [1400, 7000], gammas=[1.1, .75])
    3395.0
    >>> bubble_at_T([0.5, 0.5], [1400, 7000], gammas=[1.1, .75], fugacities=[.995, 0.98])
    3452.440775305097
    '''
    if not fugacities:
        fugacities = [1 for i in range(len(Psats))]
    if not gammas:
        gammas = [1 for i in range(len(Psats))]
    if not none_and_length_check((zs, Psats, fugacities, gammas)):
        raise Exception('Input dimentions are inconsistent or some input parameters are missing.')
    P = sum(zs[i]*Psats[i]*gammas[i]/fugacities[i] for i in range(len(zs)))
    return P
def bubble_at_T ( zs , Psats , fugacities = None , gammas = None ) : if not fugacities : fugacities = [ 1 for i in range ( len ( Psats ) ) ] if not gammas : gammas = [ 1 for i in range ( len ( Psats ) ) ] if not none_and_length_check ( ( zs , Psats , fugacities , gammas ) ) : raise Exception ( 'Input dimentions are inconsistent or some input parameters are missing.' ) P = sum ( zs [ i ] * Psats [ i ] * gammas [ i ] / fugacities [ i ] for i in range ( len ( zs ) ) ) return P
>>> bubble_at_T([0.5, 0.5], [1400, 7000])
    4200.0
    >>> bubble_at_T([0.5, 0.5], [1400, 7000], gammas=[1.1, .75])
    3395.0
    >>> bubble_at_T([0.5, 0.5], [1400, 7000], gammas=[1.1, .75], fugacities=[.995, 0.98])
    3452.440775305097
>>> bubble_at_T ( [ 0 . 5 0 . 5 ] [ 1400 7000 ] ) 4200 . 0 >>> bubble_at_T ( [ 0 . 5 0 . 5 ] [ 1400 7000 ] gammas = [ 1 . 1 . 75 ] ) 3395 . 0 >>> bubble_at_T ( [ 0 . 5 0 . 5 ] [ 1400 7000 ] gammas = [ 1 . 1 . 75 ] fugacities = [ . 995 0 . 98 ] ) 3452 . 440775305097