The resistance of an electrical toasterf has a temeprature dependence given by `R(T)=R_0[(T-T_0)]` in its range of operation. At `T_0=300 K,R=100Omega and at T=500 K,R=120 Omega`. The toasterf is connected to a voltage source at 200 V and its temperature is raised at a con- stant rate from 300 to 500 K in 30 s. The total work done in raising the temperature is :

Options

A. `400 ln (5)/(6) kJ`
B. `200 ln (2)/(3) kJ`
C. `60 ln ((6)/(5)) kJ`
D. `400 ln (1.5)/(1.3) kJ`

Answer

C

Explanation

Work done in 30s, `W= int_(0)^(30) (V^(2) )/( R) dt`
or `.W- int_(0)^(30) ((200)^(2))/(100(1+ alpha (20 t)/(3) ) dt = ((200)^(2) )/( 100) int_(0)^(30) (dt)/(1 + (20 alpha)/(3) t)`
`= (400 xx 3)/(20 alpha) l n ((1+ 20 alpha)/(3) xx 30)/(1) = 60,000 ln((6)/(5))`
`because 120 = 100 [1+ alpha (200)] therefore alpha= (1)/(1000)`