Two plates of same area are placed in contact. Their thickness as well as thermal conductivities are in the ratio $$2$$:$$3$$. The outer surface of one plate is maintained at $$10$$°C and that of the other at $$0$$ DC. What is the temperature at the common surface?

Question

Infinity Learn · Accepted Answer

If T is the temperature of the interface .of two plates of same area, $$thendQdt=K1A(10$$−$$T)$$Δ$$x1=K2A(T$$−$$0)$$Δ$$x2or$$   $$K1A(10$$−$$T)$$Δ$$x1=32K1A(T$$−$$0)3/2$$Δ$$x1$$ ∵$$K1K2=23$$ and Δ$$x1$$Δ$$x2=23or$$   $$10$$−$$T=T$$−$$0$$ or $$T+T=10$$ or $$2T=10$$∴ $$T=5$$∘C

Two plates of same area are placed in contact. Their thickness as well as thermal conductivities are in the ratio 2:3. The outer surface of one plate is maintained at 10°C and that of the other at 0 DC. What is the temperature at the common surface?

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