Question

A large spherical enclosure has a small opening. The rate of emission of radiative flux through this opening is 5.67 kw/m2. The temperature (in c, up to 1 decimal place) at the inner surface of the sphere will be about _____________.

Answer 1

Answer:

The temperature at the inner surface of the sphere will be about -95.7°C.

Explanation:

We will solve this question by Stefan-Boltzmann Law. Which states that "the total radiant heat power emitted from the surface is proportional to the fourth power of its absolute temperature".i.e.

P$/$A=σT⁴    (1)

Where,

P= Power of emission in watt

A= Area

σ=Stefan-Boltzmann constant=5.67×10⁻⁸W/m²K⁴

T=Temperature in Kelvin

The value given in question for P$/$A is 5.67kW/m². Let's substitute this value in equation (1);

5.67×10³=5.67×10⁻⁸×T⁴

T⁴=10¹¹

T=100×1.778=177.8K

Now to convert it into celsius we need to subtract it by 273.5K;

T°C=177.8-273.5=-95.7°C

Hence, The temperature at the inner surface of the sphere will be about -95.7°C.