We present the first full FIR spectrum of Centaurus A (NGC 5128) from 43 - 196.7 um. The data was obtained with the ISO Long Wavelength Spectrometer (LWS). We conclude that the FIR emission in a 70 arcsec beam centred on the nucleus is dominated by star formation rather than AGN activity. The flux in the far-infrared lines is ~ 1 % of the total FIR: the [CII] line flux is ~ 0.4 % FIR and the [OI] line is ~ 0.2 %, with the remainder arising from [OIII], [NII] and [NIII] lines. These are typical values for starburst galaxies. The ratio of the [NIII]/[NII] line intensities from the HII regions in the dust lane can be modelled as a ~ 6 million year old starburst. This suggests that the galaxy underwent either a recent merger or a merger which triggered a series of bursts. We estimate that < 5 % of the observed [CII] arises in the cold neutral medium (CNM) and that ~ 10 % arises in the warm ionized medium (WIM). The main contributors to the [CII] emission are the PDRs, which are located throughout the dust lane and in regions beyond where the bulk of the molecular material lies. On scales of ~ 1 kpc the average physical properties of the PDRs are modelled with a gas density, n ~ 1000 cm^-3, an incident far-UV field, G ~ 100 times the local Galactic field, and a gas temperature of ~ 250 K.
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