Question

The height up to which water will rise in a capillary tube will be
A) Minimum when water temperature is ${4^0}C$
B) maximum when water temperature is ${4^0}C$
C) maximum when water temperature is ${0^0}C$
D) Minimum when water temperature is ${0^0}C$

Answer 1

Hint
To find the height up to which water will rise in a capillary tube, it can be simply find using the formula i.e. The height of the rise in the capillary-
$h = \dfrac{{2T\cos \theta }}{{r\rho g}}$.
So here using the correlation between the L.H.S. and R.H.S. We can easily find the height.

Complete step by step answer
The height of the rise in the capillary is given by-
$h = \dfrac{{2T\cos \theta }}{{r\rho g}}$
Here, $h$ = elevation of the liquid
$T$ = surface tension
$\theta$ = angle of the concoct of the liquid with capillary tube
$Ρ$ = density of the liquid
$G$ = standard acceleration due to the gravity
$R$ = radius of the capillary tube
So here from the above equation we can see that elevation of the liquid in the capillary tube ($h$) is inversely proportional to the density of the liquid. So we can understand that greater the density lower the elevation of the liquid and we all know that density of the water is maximum at ${4^0}C$ so the elevation of the height will be minimum ${4^0}C$.
So the correct answer is option (A) Minimum when water temperature is ${4^0}C$.

Note
A capillary tube is nothing but a long, fixed –length tube with a very small diameter that is installed between the condenser and the evaporator. The capillary tube actually meters the refrigerant from the condenser to the evaporator. Capillary action (sometimes capillarity, capillary motion) is the ability of the liquid to flow in narrow spaces without the assistance of, or even in the opposition to, external forces like gravity. The effect can be seen in the drawing up of the liquid between the hairs of the paint brush, in a thin tube, in porous material such as paper and plaster.