Concepts Of Physics MCQ Edition [Volume 2]PhysicsHeat Transfer
A steel rod ( K = 46 J s ⁻¹ m ⁻¹ ^ C ⁻¹ ) of length 1.0 m has one end kept in ice at 0^ C and the opposite end in boiling water at 100^ C . The rod has a cross-sectional area of 0.04 cm ^2 . Assuming there is no heat loss to the surrounding atmosphere, determine the mass of ice melting per second. The latent heat of fusion of ice is 3.36 10^5 J kg ⁻¹ .
Options
- A5.5 10⁻⁸ g s ⁻¹
- B1.8 10⁻² g s ⁻¹
- C5.5 10⁻⁵ g s ⁻¹
- D5.5 10⁻² g s ⁻¹
Correct answer
C. 5.5 10⁻⁵ g s ⁻¹
Step-by-step solution
The rate of heat transfer through the rod is given by Fourier's law of heat conduction: H = KA(T₁ - T₂) L Substituting the given values: K = 46 J s ⁻¹ m ⁻¹ ^ C ⁻¹ A = 0.04 cm ^2 = 4 10⁻⁶ m ^2 T₁ - T₂ = 100^ C - 0^ C = 100^ C L = 1.0 m H = 46 4 10⁻⁶ 100 1.0 = 1.84 10⁻² J s ⁻¹ The heat transferred per second is used to melt the ice. The mass of ice melting per second m is given by: m = H L_f Given the latent heat of fusion of ice L_f = 3.36 10^5 J kg ⁻¹ : m = 1.84 10⁻² 3.36 10^5 kg s ⁻¹ m 5.476 10⁻⁸ kg s ⁻¹ Convertin