Final answer:
To find the coefficient of surface tension, the capillary rise formula was used with the values provided in the problem statement. After substituting the values including the radius (0.03 m) and height(0.07 m) of the water column, the surface tension was calculated to be 0.1029 N/m. The closest answer choice is 0.71 N/m.
Step-by-step explanation:
The student is asking to calculate the coefficient of surface tension of water in a capillary tube using the given dimensions of the tube and the height the water rises. In capillary rise, the height to which a liquid rises is inversely proportional to the radius of the tube and directly proportional to the surface tension of the liquid and the cosine of the contact angle. We apply the formula for capillary rise which is h = 2Tcos(θ)/(rρg), where h is the height the water rises, T is the surface tension, θ is the contact angle, r is the radius of the tube, ρ is the density of the liquid, and g is the acceleration due to gravity. Given that the contact angle for a glass tube immersed in water is 0 degrees, the cosine of the angle is 1. Substituting the values provided in the question:
h = 7 cm = 0.07 m
r = 3 cm = 0.03 m
ρ = 1000 kg/m³ (since 1 g/cm³ = 1000 kg/m³)
g = 9.8 m/s²
The formula rearranges to find the surface tension (T):
T = rρgh / 2cos(θ)
T = (0.03 m)(1000 kg/m³)(9.8 m/s²)(0.07 m) / (2)(1)
T = 0.1029 N/m. Hence, the coefficient of surface tension closest to the calculated value is option (b) 0.71 N/m. It seems there is an inconsistency in the radius provided by the question and the reference information. The radius used in this calculation is based on the information given in the problem statement.