$(6$ pts$)$ In a laboratory, a constant head permeability test was conducted on brown sand with a trace of mica. For the constant head permeameter, the following data were obtained:

Quantity of water discharged during the test

Length of specimen between manometer outlets

$=250c{m}^3$

$=11\mathrm{.}43cm$

Time required for given quantity of water to be discharged $=75sec.$

Head difference $($difference between manometer levels$)$

Temperature of water at the time of experiment

$=5\mathrm{.}5cm$

$=26C$

$=10\mathrm{.}16cm$

a$.$ Determine the hydraulic conductivity $(c\frac{m}{s})$ at the time of testing $($i$.$e$.,$ at $26C)$

b$.$ Determine the hydraulic conductivity $(c\frac{m}{s})$ at $20C.$

c$.$ At which temperature, the k value is smaller and why $($you may research on the internet$)?$