Final answer:
To calculate the excess pressure inside a mercury drop with a diameter of 4.00 mm and a surface tension of 465 dyn/cm, we use the Young-Laplace equation and find that the excess pressure is 465 Pa.
Step-by-step explanation:
The student is asking how to calculate the excess pressure inside a drop of mercury that is 4.00 mm in diameter, given that mercury has an unusually high surface tension.
The value of the surface tension is given as 465 dyn/cm, and we will apply the Young-Laplace equation, which relates the pressure difference between the inside and outside of a drop to its surface tension and size.
Calculation of Excess Pressure
To find the excess pressure (∆P), we use the following form of the Young-Laplace equation for a spherical drop:
∆P = (2 × Surface Tension) / radius
First, we must convert the diameter to the radius by dividing it by 2, so:
Radius = Diameter / 2 = 4.00 mm / 2 = 2.00 mm = 0.2 cm
Next, we can insert the values into the equation:
∆P = (2 × 465 dyn/cm) / 0.2 cm = 930 dyn/cm / 0.2 cm = 4650 dyn/cm²
To give the answer in more commonly used units, we can convert dyn/cm² to Pascals (1 dyn/cm² = 0.1 Pa):
∆P = 4650 dyn/cm² × 0.1 Pa/dyn/cm² = 465 Pa
Therefore, the excess pressure inside a mercury drop of 4.00 mm diameter is 465 Pa.