A sphere of ice at 0°C having initial radius R is placed in an environment having ambient temperature > 0°C. The ice melts uniformly, such that shape remains spherical. After a time ‘t’ the radius of the sphere has reduced to r. Assuming the rate of heat absorption is proportional to the surface area of the sphere at any moment, which graph best depicts r (t).
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The rate of heat absorption (dQ/dt) is proportional to surface area: dQ/dt ∝ 4πr². This heat melts the ice, so dQ = -L·dm, where dm is mass change. Since m = (4/3)πr³ρ, we get dm = 4πr²ρ dr.
Combining: dQ/dt = -L dm/dt = -L·4πr²ρ (dr/dt). But dQ/dt = k·4πr², so:
Simplifying: dr/dt = -k/(Lρ) = constant. Thus r decreases linearly with time: r = R - Ct.
Final answer: The graph showing a straight line with negative slope (option 2).