Cool water at 15°C is throttled from 5(atm) to 1(atm), as in a kitchen faucet. What is the temperature change of the water? What is the lost work per kilogram of water for this everyday household happening? At 15°C and 1(atm), the volume expansivity β for liquid water is about 1.5 × 10−4 K−1. The surroundings temperature Tσ is 20°C. State carefully any assumptions you make. The steam tables are a source of data.

the lost work per kilogram of water for this everyday household happening = 0.413 kJ/kg

Explanation:

Given that:

Initial Temperature = 15°C

Initial Pressure = 5 atm

Final Pressure = 1 atm

Data obtain from steam tables of saturated water at  15°C are as follows:

Specific volume  v = 1.001 cm³/gm

The change in temperature = 2°C

Specific heat of water = 4.19 J/gm.K

volume expansivity β = 1.5 × 10⁻⁴ K⁻¹

The expression to determine the change in temperature can be given as :

Δ T = 0.093 K

Now; we can calculate the lost work bt the formula:

where ;

is the temperature of the surrounding. = 20°C = (20+273.15)K =  293.15 K

From above the change in entropy is:

Thus, the lost work per kilogram of water for this everyday household happening = 0.413 kJ/kg

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