Question

Two discharge tubes have idential 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 th epotential 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?

Answer 1

$V=f\left(Pd\right),v_s=P_s{d}_s,v_L=P_l{d}_l\frac{V_s}{V_l}=\frac{P_s}{P_l}\times \frac{d_s}{d_l}\Rightarrow \frac{100}{100}=\frac{10}{20}\times \frac{1mm}{x}\Rightarrow \frac{20}{10}=\frac{1mm}{x}\Rightarrow x=\frac{1mm}{2}=0.5mm$