1 L of water at 20degrees Celsius will occupy what volume at 80 degrees Celsius? Water has a volume expansion coefficient of 210x10^-6/degree Celsius.
A) 1.6 L
B) 1.013 L
C) 0.987 L
D) 0.9987 L
For every raise in degree of temperature, water will expand by the coefficient of volume expansion times the initial volume.
At 20 degree the volume of water = 1 liter
At 80 degree the raise in temperature = 80-20 = 60 C
Therefore, the expanded volume of water.1 liter + 1 liter*coefficient of volume expansion of water * raise in temperature
=1liter + 1liter*210*10^-6* 60
= 1.0126 liter.
Initial volume of water = v = 1 L
Initial temperature = t = 20 degree C
Final temperature = t' = 80 degree C
Volume expansion coefficient = E = 210*10^-6
Let v' be the temperature at final temperature t'
Then v' is given by the formula:
v' = v[(1 + (t' - t)*E] = 1 + (80 - 20)*(210*10^-6)
= 1 + 126*10^-4 = 1 + 0.0126 = 1.0126 L
= 1.013 L (Rounding off to the third decimal place)
The water will occupy 1.013 L at 80 degree C. Therefore option B) in the given choices is correct.