We present a far infrared gas spectrometer which uses a thin film pyroelectric detector integrated on silicon. The detector is in-house fabricated and consists of 1 x 50 elements of sol-gel deposited, zirconium rich lead titanate (PZT) which are suspended on a submicron membrane for thermal insulation. The detector shows a detectivity of 16 mu A/W and is mounted into a Oriel monochromator fitted with gratings for the 3-5 mu m and the 8-12 mu m range, respectively. The infrared radiation is emitted by a hot filament and chopped mecanically with a frequency of 10 Hz. Absorption spectra of CO and CO2 gas as examples for the 3-5 mu m wavelength range show detection limits of 15 ppm for CO2 and 200 ppm for CO. Line shape investigations show that the cross sensitivity of our instrument can be neglected. In the 8-12 mu m wavelength range, we present absorption measurements for butane gas and N2O, respectively.