MHT CET · Physics · Thermal Properties of Matter
Two rods of same length & material transfer a given amount of heat in 12 s when they are joined end to end. But when they are joined length wise parallel to each other they will transfer same amount of heat in same condition in time
- A 24 s
- B 3 s
- C 1.5 s
- D 48 s
Answer & Solution
Correct Answer
(B) 3 s
Step-by-step Solution
Detailed explanation
Let the heat transferred be Q
When rods are joined end to end, heat transferred by each rod
\(=\mathrm{Q}=\frac{\mathrm{KA} \Delta \theta}{2 l} \times 12...(i)\)
When rods are joined lengthwise,
\(\mathrm{Q}=\frac{\mathrm{K} 2 \mathrm{~A} \Delta \theta}{l} \mathrm{t}...(ii)\)
From equation (i) and (ii),
\(\begin{aligned}
& \frac{\mathrm{K} 2 \mathrm{~A} \Delta \theta}{l} \mathrm{t}=\frac{\mathrm{KA} \Delta \theta}{2 l} \times 12 \\
\therefore \quad & \mathrm{t}=\frac{12}{2 \times 2}=3 \mathrm{~s}
\end{aligned}\)
When rods are joined end to end, heat transferred by each rod
\(=\mathrm{Q}=\frac{\mathrm{KA} \Delta \theta}{2 l} \times 12...(i)\)
When rods are joined lengthwise,
\(\mathrm{Q}=\frac{\mathrm{K} 2 \mathrm{~A} \Delta \theta}{l} \mathrm{t}...(ii)\)
From equation (i) and (ii),
\(\begin{aligned}
& \frac{\mathrm{K} 2 \mathrm{~A} \Delta \theta}{l} \mathrm{t}=\frac{\mathrm{KA} \Delta \theta}{2 l} \times 12 \\
\therefore \quad & \mathrm{t}=\frac{12}{2 \times 2}=3 \mathrm{~s}
\end{aligned}\)
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