Respuesta :
Answer:
The exit temperature of cold water is 37.6°C
Explanation:
Mass flow rate of water, [tex]\dot{m}_{water} = 1.2 kg/s[/tex]
Mass flow rate of air, [tex]\dot{m}_{air} = 2.5 kg/s[/tex]
[tex]T_{in} = 90^{0}C\\ T_{out} = 20^0C[/tex]
[tex]c_{air} = 1010\\c_{water} = 4186[/tex]
[tex]\dot{Q}_{lost} = 28000 J/s[/tex]
Applying the conservation of heat law between air, water and the surrounding:
[tex][\dot{m}c(T_{in} - T_{out})]_{air} = [\dot{m}c(T_{in} - T_{out})]_{water} + \dot{Q}_{lost}[/tex]
We get the exit temperature of cold water by making [tex]T_{out}[/tex] the subject of the formula above:
[tex](T_{out})_{water} =\frac{ [\dot{m}c(T_{in} - T_{out})]_{air} + [\dot{m} c T_{in}]_{water} - \dot{Q}_{lost}}{(\dot{m}c)_{water}} \\\\(T_{out})_{water} = \frac{(2.5*1010*(90-20) + [1.2*4186*(8+273)] - 28000}{1.2*4186} \\\\(T_{out})_{water} = 310.6 K\\\\(T_{out})_{water} = 37.6^0 C[/tex]
