def Gamma1_gasrad(beta):
    ''' 
    Gamma1 for a mix of ideal gas and radiation

    Hansen & Kawaler, page 177, Eqn. 3.110
    
    Parameters
    ----------
    beta : float
        Gas pressure fraction Pgas/(Pgas+Prad)

    '''
    Gamma3minus1 = (old_div(2.,3.))*(4.-3.*beta)/(8.-7.*beta) 
    Gamma1 = beta + (4.-3.*beta) * Gamma3minus1
    return Gamma1
Gamma1 for a mix of ideal gas and radiation

    Hansen & Kawaler, page 177, Eqn. 3.110
    
    Parameters
    ----------
    beta : float
        Gas pressure fraction Pgas/(Pgas+Prad)