Question

A liquid completely fills a 500.00 cm3 cup at 30.0 oC. How much more liquid could be added to the cup if liquid and cup are cooled to – 10 oC? The coefficient of volume expansion of the cup material is 19 X 10 – 6 1/ oC and the coefficient of volume expansion of the liquid is 1.5 X 10 – 4 1/ oC.

Answer 1

When the Temperature is decreased from 30 degree celsius to -10 degree calsius then

Change in Volume of cup will be

where = coefficient of volume expansion of cup

then using all given values,

(Negative sign shows that Volume of Cup is decreased with decrease in temperature)

Now Change in Volume of liquid will be

where = coefficient of volume expansion of liquid

then using all given values,

(Negative sign shows that Volume of Liquid also decreases with decrease in temperature)

Since initially both liquid and cup is at same initial volume and from the calculated change in volume for cup and liquid we can see that for same temperature change, volume of liquid has decreased more than that of cup. Thus more amount of liquid which can be added will be

  

where V_nc= New volume of cup

V_nl= New volume of liquid

then   

(ANS)