Gas density relation

Density =mass/volume,if temperature increases keeping mass and volume same then density remains same,But if we have medium size rigid cylinder containing gas,At the top and bottom of the cylinder there is copper tube which connects top and bottom of the cylinder.the cylinder and tube is the same system and contain gas at same pressure and temperature .Then what will happen if we increases the temperature of the tube only (by keeping cylinder and gas inside the cylinder at the initial temperature), the temperature of gas inside the tube increases then there will be any change in Density of gas of the tube as compared to density of gas inside the cylinder. in this question volume and mass is constant and also final pressure of the tube and cylinder will remain same.