Two identical rods are connected between two containers, one of them is at and another is at . If rods are connected in parallel then the rate of melting of ice is gm/sec. If they are connected in series then the rate is . The ratio is [2

Question

Two identical rods are connected between two containers, one of them is at $100 ° C$ and another is at $0 ° C$ . If rods are connected in parallel then the rate of melting of ice is $q_{1}$ gm/sec. If they are connected in series then the rate is $q_{2}$ . The ratio $\frac{q_{2}}{q_{1}}$ is [2004]

Smart Achievers · Accepted Answer

(4)

In parallel combination of rods

$K_{P} = K_{1} + K_{2} = K + K = 2 K$

In series combination

$K_{S} = \frac{K_{1} - K_{2}}{K_{1} + K_{2}} = \frac{K K}{2 K} = \frac{K}{2}$

$q_{1} = \frac{2 K A (100)}{ℓ} and q_{2} = \frac{K A (100)}{2 ℓ}$

$∴$ $\frac{q_{2}}{q_{1}} = \frac{K A (100)}{2 ℓ} \times \frac{ℓ}{2 K A (100)} = \frac{1}{4}$

Solution

1 2

2 4

3 1/2

4 1/4

Want Us to Email you About Special Offers & Updates?

Solution

Q. Two identical rods are connected between two containers, one of them is at 100°C and another is at 0°C. If rods are connected in parallel then the rate of melting of ice is q1 gm/sec. If they are connected in series then the rate is q2. The ratio q2q1 is [2004]

1 2

2 4

3 1/2

4 1/4

Ans. (4) In parallel combination of rods KP=K1+K2=K+K=2K In series combination KS=K1-K2K1+K2=KK2K=K2 q1=2KA(100)ℓ and q2=KA(100)2ℓ ∴ q2q1=KA(100)2ℓ×ℓ2KA(100)=14

Want Us to Email you About Special Offers & Updates?