A 500cm3 pyrex beaker is 95% full of methanol at 5 degree celcius at what temperature will it be 100% full with methanol

  40.3 °C

Explanation:

The volumetric coefficient of expansion of methanol is reportedly about 0.00149/K at 20 °C. Ordinarily, these coefficients vary with temperature, but we'll assume it is constant and that the expansion is linear with temperature.

Then we want to find the change in temperature ΔT such that ...

  95%(1 +0.00149·ΔT) = 100%

  0.0014155·ΔT = 0.05 . . . . simplify, subtract 95%

  ΔT = 0.05/0.0014155 ≈ 35.3

Adding this temperature change to the original 5 °C tells us the beaker will be full with methanol if heated to ...

  5 °C +35.3 °C = 40.3 °C

The beaker itself expands when heated. Its linear coefficient of expansion is about 3.3×10^-6/K, so its volume expansion over the temperature range of interest is on the order of 1 part in 3000. This is far smaller than any of the other errors associated with this calculation or with determination of "100% full". We choose to ignore it.

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