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Mechanical Properties Of Fluids

Question
CBSEENPH11019357

A brass rod and a steel rod are both of length 1.2 m at room temperature 30°C. Both the rods are put in boiling water. Find the difference in the length of two rods in boiling water, αb = 1.8 x 10–5°C–1 and αs=l.2 x 10–5°C–1.

Solution
The length L of the rod when heated by straight theta°C increases to L' given by, 
                    straight L apostrophe space space equals space straight L left parenthesis 1 plus αθ right parenthesis 
∴ straight L apostrophe subscript straight s space equals space straight L subscript straight s left parenthesis 1 plus straight alpha subscript straight s straight theta right parenthesis space space space and space space space straight L apostrophe subscript straight b space equals space straight L apostrophe subscript straight b left parenthesis 1 plus straight alpha subscript straight b straight theta right parenthesis 
Here lengths of the two rods are equal, 
∴      straight L apostrophe subscript straight s space equals space straight L left parenthesis 1 plus straight alpha subscript straight s straight theta right parenthesis space space space space space space space space and space space space straight L apostrophe subscript straight b space equals space straight L subscript straight b left parenthesis 1 plus straight alpha subscript straight b straight theta right parenthesis 
The difference in length of the two rods, 
increment straight L space equals space straight L apostrophe subscript straight b minus straight L apostrophe subscript straight s

space space space space space space space equals space straight L left parenthesis straight alpha subscript straight b minus straight alpha subscript straight s right parenthesis straight theta       
   
     equals 1.2 cross times left parenthesis 1.8 cross times 10 to the power of negative 5 end exponent minus 1.2 cross times 10 to the power of negative 5 end exponent right parenthesis cross times 70 space

equals 5.04 cross times 10 to the power of negative 4 end exponent straight m