A student measures the capillary rise height h for various tubes of different radii r using two different liquids, A and B . Both liquids have the same density and a contact angle of zero. The student plots a graph of h (on the y-axis) versus 1 r (on the x-axis). The graph yields two straight lines passing through the origin. The line for liquid A makes an angle of 60^ with the x-axis, while the line for liquid B mak

Step-by-step solution

The formula for capillary rise is given by h = 2T g r . Rearranging this, we get h = ( 2T g ) 1 r . When h is plotted against 1 r , the slope of the straight line is m = 2T g . For the two liquids, the density and contact angle = 0^ are the same. Thus, the surface tension T is directly proportional to the slope m . The slope is given by , where is the angle made with the x-axis. For liquid A, m_A = (60^ ) = 3 . For liquid B, m_B = (30^ ) = 1 3 . The ratio of their surface tensions is T_A T_B = m_A m_B = 3 1 3 = 3 .