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Assoli18 [71]
3 years ago
6

29. 2072 Set C Q.No. 10c

Physics
1 answer:
Annette [7]3 years ago
6 0

Answer:

90.2^{\circ}C

Explanation:

Considering the thermal conductivity of aluminium and brass as k_{al}=205 W/mK and k_{br}=109 W/mk respectively  

The temperature at the end of aluminium and brass are given as T_{al}=150^{\circ}C and T_{br}=20^{\circ}C respectively with length of rod L=1.3 m , Length of aluminium L_{al}=0.8 m, length of brass L_{br}=0.5 m and letting temperature at steady state be T

At steady state, thermal conductivity of both aluminium and brass are same hence

H_{br}=H_{al}

k_{al}A\frac {T_H-T}{L_{al}}= k_{br}A\frac {T-T_H}{L_{br}}

Upon re-arranging

T=\frac {k_{al}L_{al}T_{br}+k_{al}L_{br}T_{al}}{k_{br}L_{al}+k_{al}L_{br}}

(205)\frac {150-T}{0.8}=109\frac {T-20}{0.5}

T=\frac {(109*0.8*20)+(205*0.5*150)}{(109*0.8)+(205*0.5)}

T=90.2^{\circ}C

Therefore, the temperatures at which the metals are joined is 90.2^{\circ}C

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