Three metal rods of same length and same area of cross section are joined in series. Their thermal conductivities are in the ratio 2 : 4 : 3. In the steady state if the temperature of the junctions are 116°C and 74°C then temperature difference between the two free ends is

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

200°C

180°C

182°C

218°C

answer is C.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Three rods are in the series so heat flow will be same $\frac{K A (T_{1} - T_{2})}{l} =$ constant, as their dimensions are also same so $K (T_{1} - T_{2})$ is constant.

if the temperature at the free end of first rod is $T_{a}$ and temperature of the junction first and second is $T_{12}$ and temperature of the junction second and third is $T_{23}$ and temperature of the free end of third is $T_{b}$ then

$\begin{array}{rcl} 2 K (T_{a} - T_{12}) & = & 4 K (T_{12} - T_{23}) = 3 K (T_{23} - T_{b}) \\ 2 (T_{a} - 116) & = & 4 (116 - 74) = 3 (74 - T_{b}) \\ s o l v i n g f o r T_{a} & = & 200 {}^{0}C a n d T_{b} = 18 {}^{0}C \\ so temperature difference across the free end & = & 182^{0} C \end{array}$