A rod of negligible heat capacity has length 40 cm , area of cross-section 1.0 cm 2 and thermal conductivity 100 W / m ∘ C . The temperature of one end is maintained at 0 ∘ C and that of the other end is slowly and linearly varied from 0 ∘ C to 6 0 ∘ C in 10 minutes. Assuming no loss of heat through the sides, find the total heat transmitted through the rod in these 10 minutes (in J).

d t d Q = L k A Δ T Δ T a vg = 2 0 + 60 = 3 0 0 C Q = ( L k A Δ T a vg ) × t Q = ( 0.4 100 × 1 0 − 4 × 30 ) × 600 Q = ( 0.4 0.3 ) × 600 = 0.75 × 600 = 450J

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A rod of negligible heat capacity has length 40 cm , area of cross-section $1.0 cm^{2}$ and thermal conductivity $100 W / m^{\circ} C$ . The temperature of one end is maintained at $0^{\circ} C$ and that of the other end is slowly and linearly varied from $0^{\circ} C$ to $6 0^{\circ} C$ in 10 minutes. Assuming no loss of heat through the sides, find the total heat transmitted through the rod in these 10 minutes (in J).

Answer:

4500

Solution:

$\frac{d Q}{d t} = \frac{k A Δ T}{L}$

$Δ T_{a vg} = \frac{0 + 60}{2} = 3 0^{0} C$

$Q = (\frac{k A Δ T _{a vg}}{L}) \times t$

$Q = (\frac{100 \times 1 0 ^{- 4} \times 30}{0.4}) \times 600$

$Q = (\frac{0.3}{0.4}) \times 600 = 0.75 \times 600 = 450J$

Stream:JEESubject:PhysicsTopic:Heat & ThermoSubtopic:Calorimetry

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