A human body has a surface area of approximately 1 m ^ 2 . The...

A human body has a surface area of approximately

1{m}^{2}

. The normal body temperature is

10K

above the surrounding room temperature

{T}_{0}

. Take the room temperature to be

{T}_{0} = 300K

. For

{T}_{0} = 300K

, the value of

\sigma{T}^{4} = 460\dfrac{W}{{m}^{2}}

(where

\sigma

is the Stefan-Boltzmann constant). Which of the following options is/are correct?

Options

AIf the surrounding temperature reduces by a small amount ${ΔT}_{0} < < {T}_{0}$ , then to maintain the same body temperature the same (living) human being needs to radiate $ΔW = 4σ{T}_{0}^{3}{ΔT}_{0}$ more energy per unit time
BReducing the exposed surface area of the body (e.g. by curling up) allows humans to maintain the same body temperature while reducing the energy lost by radiation.
CIf the body temperature rises significantly then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths
DThe amount of energy radiated by the body in 1 second is close to $60Joules$

Correct answer

C. If the body temperature rises significantly then the peak in the spectrum of electromagnetic radiation emitted by the body would shift to longer wavelengths

Step-by-step solution

\begin{aligned} & \text{ Energy radiated }=\sigma A\left(T^4-T_0^4\right) \mathrm{t} \\ & =\sigma A\left[\left(\mathrm{ T}_0+10\right)^4-T_0^4\right] t \\ & =\sigma A T_0^4\left[\left(1+\frac{10}{T_0}\right)^4-1\right] t \\ & =\sigma A T_0^4\left[\frac{40}{T_0}\right] \times t=460 \times 1 \times \frac{40}{300} \times 1=61.33 J \\ & P=\frac{\text{ Energy radiated }}{\text{ time }}=\sigma A T^4-\sigma A T_0^4 \\ & \therefore\left|\frac{d p}{d T_0}\right|=\sigma A\left(4 T_0^3\right) \therefore|d p|=\sigma A\left(4 T_0^3\right) d T_0 \\ & \therefore|\Delta P|=4 \sigma A T_0^3 \end{aligned}

) A, B are not correct options as human body is not a black body. Energy radiated (\propto \mathrm{A}) where (\mathrm{A}) is

the

surface area of the body. ' (\mathrm{C}) ' is the correct option$

Practice Thermal Properties of Matter on Quantrex Academy →

More from Thermal Properties of Matter

As shown in the figure, an insulated container is fitted with a thermally conducting but… JEE Advanced 2026 The heat extracted out of x gram of water initially at 50°C to cool it down to 0°C is… JEE Main 2026 The temperature of a metal strip having coefficient of linear expansion α is increased… JEE Main 2026 Which of the following best represents the temperature versus heat supplied graph for… JEE Main 2026 10 kg of ice at -10^ ∘ C is added to 100 kg of water to lower its temperature from 25 ^ ∘… JEE Main 2026 A brass wire of length 2 m and radius 1 mm at 27^ ∘ C is held taut between two rigid… JEE Main 2026 Rods x and y of equal dimensions but of different materials are joined as shown in… JEE Main 2026 An aluminium and steel rods having same lengths and cross-sections are joined to make… JEE Main 2026 Full Thermal Properties of Matter list All JEE Advanced PYQs