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JIPMER 2006
Exam
JIPMER
Year
2006
Subject
Physics
Chapter
Thermal Properties of Matter

JIPMER 2006 · Physics · Thermal Properties of Matter

Two rods of same material have same length and area. The heat Δ Q...

Two rods of same material have same length and area. The heat ΔQ\Delta Q flows through them for 12 minutes when they are joint side by side. If now both the rods are joined in parallel, then the same amount of heat ΔQ\Delta Q will flow in :Two rods of same material have same length and area. The heat Δ Q flows through them for 12 minutes when they are jointTwo rods of same material have same length and area. The heat Δ Q flows through them for 12 minutes when they are joint

Options

  1. A24 min
  2. B3 min
  3. C12 min
  4. D6 min

Correct answer

B. 3 min

Step-by-step solution

When rods are joined in series then heat flow Two rods of same material have same length and area. The heat Δ Q flows through them for 12 minutes when they are joint ΔQ1=A(T1−T2)t1l1K1+l1K2=A(T1−T2)t1lK1+lK2=A(T1−T2)t1lK2\begin{aligned} & \Delta Q_1=\frac{A\left(T_1-T_2\right) t_1}{\frac{l_1}{K_1}+\frac{l_1}{K_2}} \\ & =\frac{A\left(T_1-T_2\right) t_1}{\frac{l}{K_1}+\frac{l}{K_2}}=\frac{A\left(T_1-T_2\right) t_1}{l} \frac{K}{2}\end{aligned} When rods are joined in parallel ΔQ2=(K1A+K2A)(T1−T2)t2l=2KA(T1−T2)t2l∵ΔQ1=ΔQ2(given)\begin{aligned} \Delta Q_2 & =\left(K_1 A+K_2 A\right) \frac{\left(T_1-T_2\right) t_2}{l} \\ & =\frac{2 K A\left(T_1-T_2\right) t_2}{l} \\ \because \Delta Q_1 & =\Delta Q_2\quad(given)\end{aligned}Two rods of same material have same length and area. The heat Δ Q flows through them for 12 minutes when they are joint ∴t2=t14=124=3 min\therefore \quad t_2=\frac{t_1}{4}=\frac{12}{4}=3 \mathrm{~min}
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