Explanation Given info: The temperature coefficient of resistivity α of silver is 3.8 × 10 − 3 ( ° C ) − 1 . The reference temperature T 0 is 20.0 ° C . Write the expression of the resistivity due to change in the temperature. ρ = ρ 0 [ 1 + α ( T − T 0 ) ] (1) Here, ρ 0 is the resistivity of material at 20.0 ° C . T is the temperature of 0 ° C . ρ is the resistivity of silver. Write the expression of the resistivity due to change in the temperature. ρ = ρ 0 ′ [ 1 + α ′ ( T ) ] (2) Here, ρ 0 ′ is the resistivity of material at 0 ° C . α ′ is the temperature coefficient of silver. The formula of resistivity ρ 0 ′ is, ρ 0 ′ = ρ 0 ( 1 − T 0 α ) Substitute ρ 0 ( 1 − T 0 α ) for ρ 0 ′ in equation (2). ρ = ρ 0 ( 1 − T 0 α ) [ 1 + α ′ ( T ) ] Substitute ρ 0 [ 1 + α ( T − T 0 ) ] for ρ in above equation. ρ 0 [ 1 + α ( T − T 0 ) ] = ρ 0 ( 1 − T 0 α ) [ 1 + α ′ ( T ) ] [ 1 + α ( T − T 0 ) ] = ( 1 − T 0 α ) [ 1 + α ′ ( T ) ] 1 + α ( T − T 0 ) ( 1 − T 0 α ) = [ 1 + α ′ ( T ) ] 1 + α ( T − T 0 ) ( 1 − T 0 α ) − 1 = α ′ ( T ) Simplify the above equation

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Chapter 27, Problem 27.73AP

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The coefficient $α′$ for silver.

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Chapter 27, Problem 27.72AP

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