Question

An ordinary glass in lled to the brim with 0.6 L if water at 90◦C. If the temperature of glass and water is decreased to 30◦C, how much water could be added to the glass?

Answer 1

Given

the volume of water in a glass up to brim is V = 0.6 L , at 90 0C

if the temperature is decreased to 30 0c that is dT = 90 0C-30 0C = 60 0C

the amount of water to be added is =?

as the temperature changes the volume expansion takes place here in this case  

the change in volume of the glass and water are

for water dV_W = gamma*V*dT

where gamma is the coefficient of volume expansion = 207*10^-6 /0C

and for glass it is = 25.5*10^-6 /0C

so dV_w = 207*10^-6*0.6*60 L = 0.007452 L = 7.452 mL

and dV_g = 25.5*10^-6*0.6*60 L = 0.000918 L = 0.918 mL

so the volume of the water to be added is 7.452-0.918 mL = 6.534 mL = 0.006534 L