If 1.2 x 10^6J of heat energy is given off in 1 sec from a vessel maintained at a temperature gradient of 30Km−¹; the surface area of the vessel is?

A. 1.0 x 10²m²
B. 9. 0 x 10²m²
C. 1.0 x 10³m²
D. 9.0 x 10⁴m²

Correct Answer:

Option A – 1.0 x 10²m²

Explanation

Generally in thermal/heat conduction, if 1.2 x 10⁶ J is the heat flow per seconds; 30KM^-1 is the temperature gradient of the materials; and 400Wm^-1K^-1 the thermal conductivity of the material, then we have that:
heat flow per seconds per unit area = thermal conductivity x temp. gradient
i.e = 1.2 x 10⁶Area
= 400 x 30
=> 400 x 30 x Area = 1.2 x 10⁶
∴ Area = 1.2 x 10⁶400 x 30
Area = 100m² or 1.0 x 10²m²