Question

29. 2072 Set C Q.No. 10c

A rod 1.300 m long consists of a 0.800 m length of aluminium joined end to end to a 0.500 m
length of brass. The free end of the aluminium section is maintained at 150°C and the free end
of the brass piece is maintained at 20°C. No heat is lost through the side of the rod. At steady
state what is the temperature of the point when two metals are joined,
Ans: 90°C
30. 2071 Set D Q.No. 106
long and
min​

Answer 1

`90.2^(\circ)C`

Step-by-step 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`