Question

We stated in Example 11.12 that a xylem tube is of radius 2.50×10⁻⁵ m . Verify that such a tube raises sap less than a meter by finding h for it, making the same assumptions that sap's density is 1050 kg/m³ , its contact angle is zero, and its surface tension is the same as that of water at 20.0º C .

Answer 1

Using the given parameters and the equation for capillary action, we can calculate that the sap in a xylem tube of radius 2.50×10⁻⁵ m would rise up to approximately 0.6 m, which is less than one meter.

Step-by-step explanation:

The height to which a liquid rises when capillary action is at work can be calculated using the equation: h = 2γcosθ/(ρgr), where: h is the capillary rise (which we're solving for), γ is the surface tension, θ is the contact angle, ρ is the density of the liquid, g is the acceleration due to gravity, and r is the radius of the tube.

Given values are: the radius r = 2.50×10⁻⁵ m, the surface tension γ of water at 20.0ºC = 0.0728 N/m (standard value), the contact angle θ is 0 degrees, the density ρ of sap = 1050 kg/m³, and the acceleration due to gravity g = 9.8 m/s².

Putting these values into the equation, we get: h = 2*0.0728*cos(0)/(1050*9.8*2.5*10^-5) = approximately 0.6 m, showing that the sap in a xylem tube of this radius does indeed rise less than one meter.

Learn more about Capillary Action