The bulk modulus of water is B = 2.2 x 109 N/m2. What change in pressure ÄP (in atmospheres) is required to keep water from expanding when it is heated from 11.2 °C to 38.8 °C?
To find the change in pressure (ΔP) required to keep water from expanding when it is heated, we can use the formula:
ΔP = B * ΔV / V
Where:
- ΔP is the change in pressure,
- B is the bulk modulus of water,
- ΔV is the change in volume, and
- V is the initial volume.
In this case, we need to find the change in pressure (ΔP) to prevent water from expanding when it is heated from 11.2 °C to 38.8 °C.
To find the change in volume (ΔV), we can use the formula:
ΔV = V * β * ΔT
Where:
- ΔV is the change in volume,
- V is the initial volume,
- β is the coefficient of volume expansion for water, and
- ΔT is the change in temperature.
The coefficient of volume expansion for water (β) is given as:
β = 1 / V * ΔV / ΔT
Now, we can substitute the values into the formulas and calculate the change in pressure (ΔP).
1. Calculate ΔV:
ΔV = V * β * ΔT
ΔV = V * (1 / V * ΔV / ΔT) * ΔT
ΔV = ΔV
2. Calculate ΔP:
ΔP = B * ΔV / V
ΔP = B * (ΔV) / V
ΔP = B
Given that the bulk modulus of water (B) is 2.2 x 10^9 N/m^2, the change in pressure (ΔP) required to prevent water from expanding when heated from 11.2 °C to 38.8 °C is 2.2 x 10^9 N/m^2.