Question

Two identical square rods of metal are welded end to end as shown in figure (a). $20$ calories of heat flows through it in $4$ minutes. if the rods are welded as shown in figure (b), the same amount of heat will flow through the rods in

• A. $1$ minute
• B. $2$ minutes
• C. $4$ minutes
• D. $16$ minutes

Answer 1

The correct option is A $1$ minute

The rate at which the heat is developed is given by

$\frac{dQ}{dt}=\frac{KA\delta T}{L}$

$\frac{dQ}{dt}=\frac{KA\delta (T_1-T_2)}{2x}$

=5

Now , we have $\frac{dQ}{dt}=\frac{2KA\delta T}{x}$

Therefore by solving above we have , t=2 minutes