Answer :
Answer:
To calculate the magnitude of the heat current for a spherical blackbody, we can use the Stefan-Boltzmann law, which states that the power radiated by a blackbody is proportional to the fourth power of its absolute temperature. The formula is given by:
P=σAT4
where:
( P ) is the power or heat current in watts (W),
( \sigma ) is the Stefan-Boltzmann constant (( 5.67 \times 10^{-8} , \text{W/m}2\text{K}4 )),
( A ) is the surface area of the blackbody in square meters (m²),
( T ) is the absolute temperature in kelvins (K).
First, we need to convert the temperature from Celsius to Kelvin:
T(K)=T(°C)+273.15=20+273.15=293.15K
Next, we calculate the surface area ( A ) of the sphere:
A=4πr2
Given that the radius ( r ) is 2.6 cm, we need to convert it to meters:
r=2.6cm=0.026m
Now, we can calculate the surface area:
A=4π(0.026)2≈0.0085m2
Finally, we can calculate the power ( P ):
P=σAT4=(5.67×10−8)×0.0085×(293.15)4
Calculating this gives us the heat current in watts. Remember to keep the final answer in SI units, which for power is watts (W).
