Question

1. A rod of length 1 m having cross-sectional arca
0.75 m² conducts heat at 6000 JS' Then the
temperature difference acorss the rod is, if
K - 200 Wm'K!​

Answer 1

$\color{darkblue}\underline{\underline{\sf Given-}}$

• Lenght of rod (x) = 1m
• Cross-section Area (A) = 0.75m²
• Heat ${\sf \left(\dfrac{dQ}{dt}\right)=6000J/s}$
• Thermal conductivity (K) ${\sf = - 200W.m^{-1}K^{-1}}$

$\color{darkblue}\underline{\underline{\sf To \: Find-}}$

• Temperature difference across the rod (∆T)

━━━━━━━━━━━━━━━━━━━━━━━━

❏ Thermal Conduction

$\large\color{violet}\bullet\underline{\boxed{\sf \dfrac{dQ}{dt}=-KA\dfrac{dT}{dx}}}$

$\implies{\sf 6000=-(-200)×0.75×\dfrac{dT}{1} }$

$\implies{\sf dT=\dfrac{6000}{200×0.75}}$

$\color{red}\implies{\sf dT=40K}$

$\color{darkblue}\underline{\underline{\sf Answer-}}$

Temperature across the rod is $\color{red}{\sf 40K}$.