Question

Two ends of a conducting rod of varying cross-sections are maintained at 200 ⁰C and 0 ⁰C respectively. In steady state –

• A. Temperature difference across AB and CD are equal
• B. Temperature difference across AB is greater than that of across CD
• C. Temperature difference across AB is less than that of across CD
• D. Temperature difference may be equal or different depending on the thermal conductivity of the rod

Answer 1

Answer: (C)

Temperature difference across AB is less than that of across CD

Answer 2

Rate of flow of heat $\frac{dQ}{dt}$or H is equal throughout the rod.

Temperature difference = (H) (thermal resistance)

or

Temperature difference µ thermal resistance (R)

where R =$\frac{l}{KA}$ or R µ$\frac{1}{A}$

Area across CD is less. Therefore, temperature difference across CD will be more.