Question

The temperature dependence of the emf of a standard electrochemical cell is given by
$E=1.02-4.0\times {10}^{-5}(T-20)-9.0\times {10}^{-7}(T-20{)}^2$
where, $T$ is in ${}^{\circ }C$ and $E$ is in volts. The temperature coefficient of the emf at ${30}^{\circ }C$ is:

• A. $-5.8\times {10}^{-5}$
• B. $-9.0\times {10}^{-7}$
• C. $+6.3\times {10}^{-5}$
• D. $+9.5\times {10}^{-7}$

Answer 1

Answer: (A)

$-5.8\times {10}^{-5}$

$\frac{dE}{dT}=\frac{d}{dT}[1.02-4\times {10}^{-5}(T-20)-9.0\times {10}^{-7}(T-20)$
$=-0.4\times {10}^{-5}-9\times {10}^{-7}\times 2T$
$=-0.4\times {10}^{-5}-9\times {10}^{-7}\times 2\times 30(\because T={30}^{\circ }C)$
$=-5.8\times {10}^{-5}$.