A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat Q in time t . The metallic rod is - Physics MCQ Physics | ExamTest.live

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A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat Q in time t . The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod, when placed in thermal contact with the two reservoirs in time t ?

A $Q /2$
B $4 Q$
C $16 Q$
D $Q /16$

Solution & Step-by-step Explanation

Rate of heat flow H = \frac{Q}{t} = \frac{k A Δ T}{L} . When melted and reshaped, volume V = A L remains constant. New radius r^{'} = r /2 ⟹ New area A^{'} = π (r /2)^{2} = A /4 . Since volume is constant, A \cdot L = A^{'} \cdot L^{'} $ A \cdot L = (A /4) \cdot L^{'} ⟹ L^{'} = 4 L N e w r a t eo f h e a t f l o w Q' : Q^{'} \propto \frac{A ^{'}}{L ^{'}} $ \frac{Q ^{'}}{Q} = \frac{A ^{'}}{A} \times \frac{L}{L ^{'}} = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} Q^{'} = Q /16

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A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat Q in time t . The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod, when placed in thermal contact with the two reservoirs in time t ?

Q /2

4 Q

16 Q

Q /16

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