The resistance of an electrical toaster has a temperature dependence given by R T = R 0 1 + α T - T 0 in its range of operation. At T 0 = 300 K , R = 100 Ω and a t T = 500 K , R = 120 Ω . The toaster is connected to a voltage source at 200 V and its temperature is raised at a constant rate from 300 to 500 K in 30 s . The total work done in raising the temperature is : Note: This question was awarded as

Step-by-step solution

P = V 2 R = 200 2 R 0 [ 1 + α ( T - T 0 ) ] T → temperature at 't' T 0 = 300K → temperature at t = 0 T - T 0 = 5 0 0 - 3 0 0 3 0 t T - T 0 = 2 0 0 3 0 t T - T 0 = 2 0 t 3 α = 1 R 0 ∆ R ∆ T = 1 100 20 200 = 10 - 3 K         H = ∫ P d t = ∫ 0 3 0 2 0 0 2 1 0 0 1 + α 2 0 t 3 dt = 2 0 0 × 2 0 0 1 0 0 ∫ 0 3 0 dt 1 + 2 0 α 3 t = 4 0 0 × 3 2 0 α ℓ n ( 1 + 20 ∝ 3 × 30 1 ) = 6 0 0 0 0  ℓ n&#16