Surface Tension

Step 1: Understanding the volume conservation principle When two soap bubbles coalesce under isothermal conditions, the process follows the principle of volume conservation: where: - (volume of first bubble) - (volume of second bubble)

Step 2: Calculating the new total volume

Step 3: Applying the radius-volume relation for bubbles Since the volume of a sphere is given by: The radius of the final bigger bubble is given by: where: The volume of the bigger bubble formed is given by:

Step 4: Verifying the correct option Comparing with given options, the correct answer is:

Step 1: Understanding Black Body Radiation The power radiated by a black body follows Stefan-Boltzmann law: where: - is the radiated power, - is the Stefan-Boltzmann constant, - is the surface area of the radiating body, - is the temperature in Kelvin.

Step 2: Calculating the Power Radiated by the Inner Sphere The inner sphere has radius , so its surface area is: The power radiated by the inner sphere:

Step 3: Absorption by the Outer Sphere The outer sphere completely surrounds the inner sphere and absorbs all the radiation. Thus, the rate of absorption of radiant energy by the outer sphere is equal to the power radiated by the inner sphere:

Step 4: Verifying the Correct Option Comparing with the given options, the correct answer is: