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Question
The sap in trees, which consists mainly of water in summer, rises in a system of capillaries of radius r = 2.5 × 10–5 m. The surface tension of sap is T = 7.28 × 10–2 Nm–1 and the angle of contact is 0°. Does surface tension alone account for the supply of water to the top of all trees?
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Solution
Radius of capillarity r = `2.5 xx 10^-5` m
S = T = `7.8 xx 10^-2 Nm^-1`
g = 9.8 m/s2
h = `(25 cos θ)/(rpg)`
= `(2 xx 7.28 xx 10^-2 cos 0^circ)/(2.5 xx 10^-5 xx 10^3 xx 9.8)`
= `(2 xx 7.28 xx 10^(-2 + 5))/(25 xx 10^3 xx 98)`
h = `(104 xx 10^3)/(175 xx 10^3)`
= `104/175`
= 0.594 m
= 0.6 m
Most of the trees are more than 0.6 m in height. So capillary action alone cannot account for the rise of water in all other trees.
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