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A glass capillary tube with a radius of r=0.5 \mathrm{~mm} is dipped into a container of water. The water rises to a height of h=3.0 \mathrm{~cm} inside the capillary due to capillary action. Calculate the surface tension of water using the given data. If a detergent is added to the water, reducing the surface tension to 2 / 3 of its original value, calculate the new capillary rise.

Option: 1

0.05 \mathrm{~m}


Option: 2

0.04 \mathrm{~m}


Option: 3

0.01 \mathrm{~m}


Option: 4

0.02 \mathrm{~m}


Answers (1)

best_answer

Given:

  • Radius of capillary tube r=0.5 \mathrm{~mm}=0.5 \times 10^{-3} \mathrm{~m}
  •  Capillary rise h=3.0 \mathrm{~cm}=3.0 \times 10^{-2} \mathrm{~m}
  • Reduced surface tension due to detergent T^{\prime}=\frac{2}{3} \times T, where T is the original surface tension.

Step 1: Calculate the original surface tension T using the capillary rise formula:

            \begin{gathered} T=\frac{4 \times h \times r}{\pi r^2} \\ T=\frac{4 \times 3.0 \times 10^{-2} \times 0.5 \times 10^{-3}}{\pi \times\left(0.5 \times 10^{-3}\right)^2} \\ T=0.120 \mathrm{~N} / \mathrm{m} \end{gathered}

Step 2: Calculate the new surface tension T^{\prime} due to the detergent:

            \begin{gathered} T^{\prime}=\frac{2}{3} \times 0.120 \mathrm{~N} / \mathrm{m} \\ T^{\prime}=0.080 \mathrm{~N} / \mathrm{m} \end{gathered}

Step 3: Calculate the new capillary rise h^{\prime} using the reduced surface tension T^{\prime} :

            \begin{gathered} h^{\prime}=\frac{T^{\prime}}{4 \times r} \\ h^{\prime}=\frac{0.080 \mathrm{~N} / \mathrm{m}}{4 \times 0.5 \times 10^{-3} \mathrm{~m}} \\ h^{\prime}=0.040 \mathrm{~m} \end{gathered}

The surface tension of water (T) is 0.120 \mathrm{~N} / \mathrm{m}. After adding the detergent, the new capillary rise \left(h^{\prime}\right) is 0.040 \mathrm{~m}.

Posted by

Pankaj Sanodiya

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