Question #2146

An Aluminum cup of 100cm[sup]3[/sup] capacity, is completely filled with ethanol at 25 degree C. How much ethanol, if any, will spill out of the cup if the temperature of both cup and ethanol is decreased to 22 degree C?

Expert's answer

Coefficient of volumeric thermal expansion of aluminium - 72x10-6 K-1

Coefficient of volumeric thermal expansion of ethanol - 750x10-6 K-1

<img src="/cgi-bin/mimetex.cgi?%5CDelta%20V_%7Bethanol%7D%20-%20%5CDelta%20V_%7Bal%7D%20=%20%28%5Calpha_%7Beth%7D%20-%20%5Calpha_%7Bal%7D%29%5CDelta%20T%20V%20=%20%28750%20-%2072%29%5Ctimes%2010%5E%7B-6%7D[1/K]*3[K]*100[cm%5E3]=%200.2034%20%5C%20[cm%5E3]" title="\Delta V_{ethanol} - \Delta V_{al} = (\alpha_{eth} - \alpha_{al})\Delta T V = (750 - 72)\times 10^{-6}[1/K]*3[K]*100[cm^3]= 0.2034 \ [cm^3]">

Coefficient of volumeric thermal expansion of ethanol - 750x10-6 K-1

<img src="/cgi-bin/mimetex.cgi?%5CDelta%20V_%7Bethanol%7D%20-%20%5CDelta%20V_%7Bal%7D%20=%20%28%5Calpha_%7Beth%7D%20-%20%5Calpha_%7Bal%7D%29%5CDelta%20T%20V%20=%20%28750%20-%2072%29%5Ctimes%2010%5E%7B-6%7D[1/K]*3[K]*100[cm%5E3]=%200.2034%20%5C%20[cm%5E3]" title="\Delta V_{ethanol} - \Delta V_{al} = (\alpha_{eth} - \alpha_{al})\Delta T V = (750 - 72)\times 10^{-6}[1/K]*3[K]*100[cm^3]= 0.2034 \ [cm^3]">

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