Question 333: Properties of Matter

Question

Three liquids of densities $$ho $$1, $$ho $$2  and $$ho $$3 (with $$ho $$1 > $$ho $$2 > $$ho $$3), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact $$	heta $$1, $$	heta $$2 and $$	heta $$3 obey

Accepted Answer

Capillary rise, $$h = {{2T\cos heta } \over {r ho g}}$$ For given value of T and $$r,h \propto {{\cos heta } \over ho }$$ Also, $${h_1} = {h_2} = {h_3}$$ or $${{\cos { heta _1}} \over {{ ho _1}}} = {{\cos { heta _2}} \over {{ ho _2}}} = {{\cos { heta _3}} \over {{ ho _3}}}$$ Since, $${ ho _1} > { ho _2} > { ho _3}$$, so $${\cos { heta _1} > \cos { heta _2} > \cos { heta _3}}$$ For $$0 \le heta < {\pi \over 2},{ heta _1} < { heta _2} < { heta _3}$$ Hence, $$0 \le { heta _1} < { heta _2} < { heta _3} < {\pi \over 2}$$

Answer

$${\pi  \over 2} > {	heta _1} > {	heta _2} > {	heta _3} \ge 0$$

Answer

0 $$ \le $$ $$	heta $$1 < $$	heta $$2 < $$	heta $$3 < $${\pi  \over 2}$$

Answer

$${\pi  \over 2} < {	heta _1} < {	heta _2} < {	heta _3} < \pi $$

Answer

$$\pi  > {	heta _1} > {	heta _2} > {	heta _3} > {\pi  \over 2}$$

Properties of Matter

Three liquids of densities $\rho 1, \rho 2 and \rho 3 (with \rho 1 > \rho 2 > \rho 3), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact \theta 1, \theta 2 and \theta $3 obey

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