A garden hose with the water valve shut and the nozzle closed sits in the sun, full of liquid water. Initially, the water is at 10°C and 6 bar. After some time the temperature of the water rises to 40°C. Owing to the increase in temperature and pressure and the elasticity of the hose, the internal diameter of the hose increases by 0.35%. Estimate the final pressure of the water in the hose.
For estimating PVT behavior of liquids, we will often assume constant coefficient of thermal expansion and isothermal compressibility. In that case, the differential relationship
can be integrated to give the integral relationship:
If the diameter of the hose increases by 0.35% (by a factor of 1.0035), then the cross-sectional area increases by a factor of 
Then 
Putting in the known values of ?, ?, and ?T, we have 
from which ?P = 11.33 bar. The final pressure is 17.33 bar.
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