Respuesta :
Explanation:
For an isothermal process equation will be as follows.
W = nRT ln[tex]\frac{P_{1}}{P_{2}}[/tex]
It is given that mass is 10 kg/s or 10,000 g/s (as 1 kg = 1000 g). So, calculate number of moles of water as follows.
No. of moles = [tex]\frac{mass}{\text{molar mass}}[/tex]
= [tex]\frac{10000 g/s}{18 g/mol}[/tex]
= 555.55 mol/s
= 556 mol/s (approx)
As T = [tex]50^{o}C[/tex] or (50 + 273.15) K = 323.15 K. Hence, putting the given values into the above formula as follows.
W = nRT ln[/tex]\frac{P_{1}}{P_{2}}[/tex]
= [tex]556 mol/s \times 8.314 J/ K mol K \times 323.15 K \times ln\frac{1}{10}[/tex]
= [tex]556 mol/s \times 8.314 J/ K mol K \times 323.15 K \times -2.303[/tex]
= -3440193.809 J/s
Negative sign shows work is done by the pump. Since, 1 J = 0.001 kJ. Therefore, converting the calculated value into kJ as follows.
[tex]3440193.809 J/s \times \frac{0.001 kJ}{1 J}[/tex]
= 3440.193 kJ/s
= 3451 kJ/s (approx)
Thus, we can conclude that the pump work is 3451 kJ/s.
