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Thermodynamics

# A clock which keeps correct time at $\;20^{0}C\;$ . How many seconds will it gains or loss per day when the temperature falls to $\;0^{0}C\;$ ? ( Coefficient of linear expansion of brass = $\;12\times 10^{-6}/^{0}C\;$ )

$(a)\;10.36\;sec\qquad(b)\;9.86\;sec\qquad(c)\;15.6\;sec\qquad(d)\;13.38\;sec$

Answer : $\;10.36\;sec$
Explanation :
Time lost or gained per second = $\;\large\frac{1}{2}\;\alpha \bigtriangleup t\;$ $\;(\bigtriangleup t-\;$ change in temperature $\;)$
Therefore , $\;\large\frac{time\;lost}{gained}\;$ in one day = $\;(\large\frac{1}{2} \alpha \bigtriangleup t)\;86400$
$=10.36\;sec$