Two discharge tubes have identical material structure and the same gas is filled in them. The length of one tube is 10 cm and that of the other tube is 20 cm. Sparking starts in both the tubes when the potential difference between the cathode and the anode is 100 V. If the pressure in the shorter tube is 1.0 mm of mercury, what is the pressure in the longer tube?
Let d1 and p1 be the length and pressure of short tube. Also d2 and p2 be the length and pressure of long tube.i.e. p1=1.0 mm d1=10 cm, d2=20 cm
According to Paschen’s law,
, i.e. the sparking potential of a gas in a discharge tube is the function of the product of pressure of the gas and separation between the electrodes.
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