In the diagram below, metal 1 is made of gold and metal 2 is silver. Both bars h
ID: 1486269 • Letter: I
Question
In the diagram below, metal 1 is made of gold and metal 2 is silver. Both bars have the same length and area of cross-section but their thermal conductivities are different. The temperature Th is maintained at a constant 84.0°C at the end A while the temperature Tc at the end B is maintained at 31.0°C.
(a) What is the temperature Tj at the junction of the two bars? The thermal conductivity of gold is 318 J/(s · m · °C) and that for silver is 420 J/(s · m · °C).
°C
(b) If metals 1 and 2 are now interchanged, but the values of Th and Tc are the same as in part (a), what will be the temperature of the junction?
°C
Explanation / Answer
let junction temperature be Tj.
let area of each cross section is Ac and length of each part is L.
then asuming there is no heat loss to the environment,
heat conducted from A to the junction =heat conducted from junction to B
as we know , heat conducted per unit time is given that
Q=thermal conductivity*area*temperature difference/length
hence in equation 1,
318*A*(84-Tj)/L=420*A*(Tj-31)/L
==>318*(84-Tj)=420*(Tj-31)
==>318*84-318*Tj=420*Tj-420*31
==>Tj*(420+318)=318*84+420*31=39732
==>Tj=39732/(420+318)=53.8374 degree celcius
b)
using the same method as above and just interchanging the thermal conductivity values:
420*(84-Tj)=318*(Tj-31)
==>420*84-420*Tj=318*Tj-318*31
==>420*84+318*31=Tj*(420+318)
==>Tj=61.1626 degree celcius