A hot air balloon is a sphere of radius 8 m. The air inside is at a temperature of 60°C. How large a mass can the balloon lift when the outside temperature is 20°C? (Assume air is an ideal gas, R = 8.314 J mole ^-1 K^-1, 1 atm. = 1.013×105 Pa; the membrane tension is 5 N m^-1.)

The surface tension and vapour pressure of water at 20°C is 7.28×10^-2 Nm^-1 and 2.33×103 Pa, respectively. What is the radius of the smallest spherical water droplet which can form without evaporating at 20°C?

Surface tension is exhibited by liquids due to force of attraction between molecules of the liquid. The surface tension decreases with increase in temperature and vanishes at boiling point. Given that the latent heat of vaporisation for water Lv = 540 k Cal kg^-1, the mechanical equivalent of heat J = 4.2 J cal^-1, density of water ρ w = 103 kg l –1, Avogadro’s No N_A = 6.0 × 1026 k mole –1 and the molecular weight of water MA = 18 kg for 1 k mole.

(a) estimate the energy required for one molecule of water to evaporate.

(b) show that the inter–molecular distance for water is []^1/3 and find its value.

(c) 1 g of water in the vapor state at 1 atm occupies 1601cm3. Estimate the intermolecular distance at boiling point, in the vapour state.

(d) During vaporisation a molecule overcomes a force F, assumed constant, to go from an inter-molecular distance d to d′. Estimate the value of F.

(e) Calculate F/d, which is a measure of the surface tension.

A hot air balloon is a sphere of radius 8 m. The air inside is at a temperature of 60°C. How large a mass can the balloon lift when the outside temperature is 20°C? (Assume air is an ideal gas, R = 8.314 J mole ^-1 K^-1, 1 atm. = 1.013×105 Pa; the membrane tension is 5 N m^-1.)

If a drop of liquid breaks into smaller droplets, it results in lowering of temperature of the droplets. Let a drop of radius R, break into N small droplets each of radius r. Estimate the drop-in temperature.

A wire forming a loop is dipped into soap solution and taken out so that a film of soap solution is formed. A loop of 6.28 cm long thread is gently put on the film and the film is pricked with a needle inside the loop. The thread loop takes the shape of a circle. Find the tension in the thread. Surface tension of soap solution = 0.030 N m^-1.

For a surface molecule

The capillaries shown in figure (14-E4) have inner radii 0.5 mm, 1.0 mm and 1.5 mm respectively. The liquid in the beaker is water. Find the heights of water level in the capillaries. The surface tension of water is 7.5 × 10^-2 N m^-1.

The free surface of oil in a tanker, at rest, is horizontal. If the tanker starts accelerating the free surface will be titled by an angle θ. If the acceleration is a m s^-2, what will be the slope of the free surface?

Consider a small surface area of 1 mm² at the top of a mercury drop of radius 4.0 mm. Find the force exerted on this area to) by the air above it (b) by the mercury below it and (c) by the mercury surface in contact with it. Atmospheric pressure = 1.0 × 10⁵ Pa and surface tension of mercury = 0.465 N m^-1. Neglect the effect of gravity. Assume all numbers to be exact.

Find the excess pressure inside (a) a drop of mercury of radius 2 mm (b) a snap bubble of radius 4 mm and (c) an air bubble of radius 4 mm formed inside a tank of water. Surface tension of mercury, soap solution and water are 0.465 N m^-1, 0.03 N m^-1 and 0.076 N m^-1 respectively.