NEET-XII-Physics
28: Heat Transfer
- #29The two rods shown in figure (28-E6) have identical geometrical dimensions. They are in contact with two heat baths at temperatures 100°C and 0°C. The temperature of the junction is 70°C. Find the temperature of the junction if the rods are interchanged.
Figure
Ans :
As the rods are connected in series, the rate of flow of heat will be same in both the cases.
Case 1:
Rate of flow of heat is given by
`` \frac{dQ}{dt}=\frac{KA∆T}{l}``
Rate of heat flow in rod P will be same as that in rod Q.
`` \therefore \frac{{K}_{\,\mathrm{\,p\,}}\mathit{\times }A\mathit{\times }\left(100-70\right)}{l}=\frac{{K}_{\,\mathrm{\,Q\,}}\times A\times \left(70-0\right)}{l}``
`` \Rightarrow 30{K}_{\,\mathrm{\,P\,}}=70{K}_{\,\mathrm{\,Q\,}}``
`` \Rightarrow {K}_{\,\mathrm{\,Q\,}}=\frac{3}{7}{K}_{\,\mathrm{\,P\,}}......\left(\,\mathrm{\,i\,}\right)``
Case 2:
Again, the rate of flow of heat will be same in rod P and Q.
`` \therefore \frac{{K}_{\,\mathrm{\,Q\,}}\times A\times \left(100-\,\mathrm{\,T\,}\right)}{l}=\frac{{K}_{\,\mathrm{\,P\,}}\times A\times \left(\,\mathrm{\,T\,}-0\right)}{l}``
`` 100{K}_{\,\mathrm{\,Q\,}}-{K}_{\,\mathrm{\,Q\,}}\,\mathrm{\,T\,}={K}_{\,\mathrm{\,P\,}}\,\mathrm{\,T\,}``
`` 100{K}_{\,\mathrm{\,Q\,}}-{K}_{\,\mathrm{\,Q\,}}T=\frac{70}{30}{K}_{\,\mathrm{\,Q\,}}T[\,\mathrm{\,using\,}(\,\mathrm{\,i\,}\left)\right]``
`` 100-T=\frac{7}{3}T``
`` 100=\frac{10}{3}T``
`` \Rightarrow T=30°\,\mathrm{\,C\,}``
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