Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer
A rod with negligible heat capacity has a length of 20 cm , a cross-sectional area of 1.0 cm ^2 , and a thermal conductivity of 200 W m ⁻¹ ^ C ⁻¹ . One end's temperature is maintained at 0^ C , while the temperature of the opposite end is slowly and linearly varied from 0^ C to 60^ C over a period of 10 minutes. Assuming no heat is lost from the sides, determine the total heat transmitted through the rod during these
Options
- A1800 J
- B60 J
- C900 J
- D3600 J
Correct answer
A. 1800 J
Step-by-step solution
The rate of heat transfer through the rod is given by Fourier's law of heat conduction: dQ dt = KA L T Since the temperature of one end is maintained at 0^ C and the other end varies linearly from 0^ C to 60^ C over 10 minutes ( 600 s ), the temperature difference T as a function of time t is T(t) = 60 600 t = 0.1 t . The total heat transmitted Q over the time interval t = 0 to t = 600 s is: Q = ₀⁶⁰⁰ KA L T(t) dt Substituting the given values K = 200 W m ⁻¹ ^ C ⁻¹ , A = 1.0 10⁻⁴ m ^2 , and L = 0.2 m : KA L = 200 10