Um termômetro tem o bulbo e o tubo capilar de vidro e contém um volume V0 de mercúrio. Uma variação na temperatura de DeltaT altera o nível de mercúrio no tubo capilar de Deltah. Considerando ϒHg o coeficiente de dilatação volumétrica do mercúrio e alpha_V o coeficiente de dilatação linear do vidro, e desprezando as variações na área do tubo capilar e os efeitos de capilaridade e tensão superficial, seu diâmetro interno é igual a 

The correct answer is A) $sqrt{frac{4V_0Delta T}{piDelta h}left(gamma_{Hg} - 3alpha Vright)}$.

To understand why this is the correct answer, let's analyze the problem step by step. We have a thermometer with a bulb and a capillary tube of glass, containing a volume $V_0$ of mercury. When the temperature changes by $Delta T$, the mercury level in the capillary tube changes by $Delta h$. We need to find the internal diameter of the capillary tube.

The key to solving this problem is to understand the concept of thermal expansion. When the temperature increases, the mercury expands, causing the level to rise in the capillary tube. The change in volume of the mercury is given by $Delta V = V_0 gamma_{Hg} Delta T$, where $gamma_{Hg}$ is the coefficient of volumetric expansion of mercury.

However, the capillary tube itself also expands due to the temperature change. The change in volume of the tube is given by $Delta V = 3alpha V_0 Delta T$, where $alpha$ is the coefficient of linear expansion of the glass. Since the tube is very thin, we can neglect the changes in its cross-sectional area and focus only on the change in its length.

The change in height of the mercury column is given by $Delta h = frac{Delta V}{A}$, where $A$ is the cross-sectional area of the tube. Substituting the expressions for $Delta V$ and rearranging, we get:$$Delta h = frac{V_0 Delta T}{A} left(gamma_{Hg} - 3alpharight)$$

Now, we can find the internal diameter of the capillary tube using the formula:$$d = sqrt{frac{4V_0Delta T}{piDelta h}left(gamma_{Hg} - 3alpha Vright)}$$

This is the correct answer, option A. The other options are incorrect because they either neglect the expansion of the tube or use the wrong formula for the change in height of the mercury column.