# A balloon is filled with 3.50 L of water at 24°C and 2.27 atm. The balloon in the figure is placed outside on a hot day. What is the volume of the balloon, assuming constant pressure?

May 23, 2016

The volume of the balloon is 3.51 L.

#### Explanation:

At first glance, this appears to be an Ideal Gas Law problem.

However, water is a liquid at 24 °C and 2.27 atm.

For argument's sake, let's say that the temperature on a hot summer day is 34 °C.

Water is essentially incompressible, but its thermal expansion may be significant.

The thermal volume coefficient (β) of water is 0.000 207/°C from 20 °C to 30 °C and 0.000 303/°C from 30°C to 40 °C.

At 30 °C,

V = V_0 +V_0βΔT = "3.50 L + 3.50 L × 0.000 207" color(red)(cancel(color(black)("°C"^"-1"))) × 6 color(red)(cancel(color(black)("°C"))) = "3.50 L + 0.0043 L" = "3.504 L"

At 34 °C,

V = V_0 +V_0βΔT = "3.504 L + 3.504 L × 0.000 303" color(red)(cancel(color(black)("°C"^"-1"))) × 4 color(red)(cancel(color(black)("°C"))) = "3.504 L + 0.0042 L" = "3.51 L"

The volume on a hot summer day is 3.51 L.