Answer:
<em>The temperature will be greater than 25°C</em>
Explanation:
In an adiabatic process, heat is not transferred to or from the boundary of the system. The gain or loss of internal heat energy is solely from the work done on the system, or work done by the system. The work done on the system by the environment adds heat to the system, and work done by the system on its environment takes away heat from the system.
mathematically
Change in the internal energy of a system ΔU = ΔQ + ΔW
in an adiabatic process, ΔQ = 0
therefore
ΔU = ΔW
where ΔQ is the change in heat into the system
ΔW is the work done by or done on the system
when work is done on the system, it is conventionally negative, and vice versa.
also W = pΔv
where p is the pressure, and
Δv = change in volume of the system.
In this case,<em> work is done on the gas by compressing it from an initial volume to the new volume of the cylinder. The result is that the temperature of the gas will rise above the initial temperature of 25°C </em>
Answer:
a)
, b) ![U_{o} \approx 0.63\,\frac{kW}{m^{2}\cdot ^{\textdegree}C}](https://tex.z-dn.net/?f=U_%7Bo%7D%20%5Capprox%200.63%5C%2C%5Cfrac%7BkW%7D%7Bm%5E%7B2%7D%5Ccdot%20%5E%7B%5Ctextdegree%7DC%7D)
Explanation:
a) The counterflow heat exchanger is presented in the attachment. Given that cold water is an uncompressible fluid, specific heat does not vary significantly with changes on temperature. Let assume that cold water has the following specific heat:
![c_{p,c} = 4.186\,\frac{kJ}{kg\cdot ^{\textdegree}C}](https://tex.z-dn.net/?f=c_%7Bp%2Cc%7D%20%3D%204.186%5C%2C%5Cfrac%7BkJ%7D%7Bkg%5Ccdot%20%5E%7B%5Ctextdegree%7DC%7D)
The effectiveness of the counterflow heat exchanger as a function of the capacity ratio and NTU is:
![\epsilon = \frac{1-e^{-NTU\cdot(1-c)}}{1-c\cdot e^{-NTU\cdot (1-c)}}](https://tex.z-dn.net/?f=%5Cepsilon%20%3D%20%5Cfrac%7B1-e%5E%7B-NTU%5Ccdot%281-c%29%7D%7D%7B1-c%5Ccdot%20e%5E%7B-NTU%5Ccdot%20%281-c%29%7D%7D)
The capacity ratio is:
![c = \frac{C_{min}}{C_{max}}](https://tex.z-dn.net/?f=c%20%3D%20%5Cfrac%7BC_%7Bmin%7D%7D%7BC_%7Bmax%7D%7D)
![c = \frac{(1\,\frac{kg}{s} )\cdot(4.186\,\frac{kW}{kg^{\textdegree}C} )}{(1.8\,\frac{kg}{s} )\cdot(4.30\,\frac{kW}{kg^{\textdegree}C} )}](https://tex.z-dn.net/?f=c%20%3D%20%5Cfrac%7B%281%5C%2C%5Cfrac%7Bkg%7D%7Bs%7D%20%29%5Ccdot%284.186%5C%2C%5Cfrac%7BkW%7D%7Bkg%5E%7B%5Ctextdegree%7DC%7D%20%29%7D%7B%281.8%5C%2C%5Cfrac%7Bkg%7D%7Bs%7D%20%29%5Ccdot%284.30%5C%2C%5Cfrac%7BkW%7D%7Bkg%5E%7B%5Ctextdegree%7DC%7D%20%29%7D)
![c = 0.541](https://tex.z-dn.net/?f=c%20%3D%200.541)
Heat exchangers with NTU greater than 3 have enormous heat transfer surfaces and are not justified economically. Let consider that
. The efectiveness of the heat exchanger is:
![\epsilon = \frac{1-e^{-(2.5)\cdot(1-0.541)}}{1-(2.5)\cdot e^{-(2.5)\cdot (1-0.541)}}](https://tex.z-dn.net/?f=%5Cepsilon%20%3D%20%5Cfrac%7B1-e%5E%7B-%282.5%29%5Ccdot%281-0.541%29%7D%7D%7B1-%282.5%29%5Ccdot%20e%5E%7B-%282.5%29%5Ccdot%20%281-0.541%29%7D%7D)
![\epsilon \approx 0.824](https://tex.z-dn.net/?f=%5Cepsilon%20%5Capprox%200.824)
The real heat transfer rate is:
![\dot Q = \epsilon \cdot \dot Q_{max}](https://tex.z-dn.net/?f=%5Cdot%20Q%20%3D%20%5Cepsilon%20%5Ccdot%20%5Cdot%20Q_%7Bmax%7D)
![\dot Q = \epsilon \cdot C_{min}\cdot (T_{h,in}-T_{c,in})](https://tex.z-dn.net/?f=%5Cdot%20Q%20%3D%20%5Cepsilon%20%5Ccdot%20C_%7Bmin%7D%5Ccdot%20%28T_%7Bh%2Cin%7D-T_%7Bc%2Cin%7D%29)
![\dot Q = (0.824)\cdot (4.186\,\frac{kW}{^{\textdegree}C} )\cdot (160^{\textdegree}C-18^{\textdegree}C)](https://tex.z-dn.net/?f=%5Cdot%20Q%20%3D%20%280.824%29%5Ccdot%20%284.186%5C%2C%5Cfrac%7BkW%7D%7B%5E%7B%5Ctextdegree%7DC%7D%20%29%5Ccdot%20%28160%5E%7B%5Ctextdegree%7DC-18%5E%7B%5Ctextdegree%7DC%29)
![\dot Q = 489.795\,kW](https://tex.z-dn.net/?f=%5Cdot%20Q%20%3D%20489.795%5C%2CkW)
The exit temperature of the hot fluid is:
![\dot Q = \dot m_{h}\cdot c_{p,h}\cdot (T_{h,in}-T_{h,out})](https://tex.z-dn.net/?f=%5Cdot%20Q%20%3D%20%5Cdot%20m_%7Bh%7D%5Ccdot%20c_%7Bp%2Ch%7D%5Ccdot%20%28T_%7Bh%2Cin%7D-T_%7Bh%2Cout%7D%29)
![T_{h,out} = T_{h,in} - \frac{\dot Q}{\dot m_{h}\cdot c_{p,h}}](https://tex.z-dn.net/?f=T_%7Bh%2Cout%7D%20%3D%20T_%7Bh%2Cin%7D%20-%20%5Cfrac%7B%5Cdot%20Q%7D%7B%5Cdot%20m_%7Bh%7D%5Ccdot%20c_%7Bp%2Ch%7D%7D)
![T_{h,out} = 160^{\textdegree}C + \frac{489.795\,kW}{(7.74\,\frac{kW}{^{\textdegree}C} )}](https://tex.z-dn.net/?f=T_%7Bh%2Cout%7D%20%3D%20160%5E%7B%5Ctextdegree%7DC%20%2B%20%5Cfrac%7B489.795%5C%2CkW%7D%7B%287.74%5C%2C%5Cfrac%7BkW%7D%7B%5E%7B%5Ctextdegree%7DC%7D%20%29%7D)
![T_{h,out} = 96.719^{\textdegree}C](https://tex.z-dn.net/?f=T_%7Bh%2Cout%7D%20%3D%2096.719%5E%7B%5Ctextdegree%7DC)
The log mean temperature difference is determined herein:
![\Delta T_{lm} = \frac{(T_{h,in}-T_{c, out})-(T_{h,out}-T_{c,in})}{\ln\frac{T_{h,in}-T_{c, out}}{T_{h,out}-T_{c,in}} }](https://tex.z-dn.net/?f=%5CDelta%20T_%7Blm%7D%20%3D%20%5Cfrac%7B%28T_%7Bh%2Cin%7D-T_%7Bc%2C%20out%7D%29-%28T_%7Bh%2Cout%7D-T_%7Bc%2Cin%7D%29%7D%7B%5Cln%5Cfrac%7BT_%7Bh%2Cin%7D-T_%7Bc%2C%20out%7D%7D%7BT_%7Bh%2Cout%7D-T_%7Bc%2Cin%7D%7D%20%7D)
![\Delta T_{lm} = \frac{(160^{\textdegree}C-78^{\textdegree}C)-(96.719^{\textdegree}C-18^{\textdegree}C)}{\ln\frac{160^{\textdegree}C-78^{\textdegree}C}{96.719^{\textdegree}C-18^{\textdegree}C} }](https://tex.z-dn.net/?f=%5CDelta%20T_%7Blm%7D%20%3D%20%5Cfrac%7B%28160%5E%7B%5Ctextdegree%7DC-78%5E%7B%5Ctextdegree%7DC%29-%2896.719%5E%7B%5Ctextdegree%7DC-18%5E%7B%5Ctextdegree%7DC%29%7D%7B%5Cln%5Cfrac%7B160%5E%7B%5Ctextdegree%7DC-78%5E%7B%5Ctextdegree%7DC%7D%7B96.719%5E%7B%5Ctextdegree%7DC-18%5E%7B%5Ctextdegree%7DC%7D%20%7D)
![\Delta T_{lm} \approx 80.348^{\textdegree}C](https://tex.z-dn.net/?f=%5CDelta%20T_%7Blm%7D%20%5Capprox%2080.348%5E%7B%5Ctextdegree%7DC)
The heat transfer surface area is:
![A_{i} = \frac{\dot Q}{U_{i}\cdot \Delta T_{lm}}](https://tex.z-dn.net/?f=A_%7Bi%7D%20%3D%20%5Cfrac%7B%5Cdot%20Q%7D%7BU_%7Bi%7D%5Ccdot%20%5CDelta%20T_%7Blm%7D%7D)
![A_{i} = \frac{489.795\,kW}{(0.63\,\frac{kW}{m^{2}\cdot ^{\textdegree}C} )\cdot(80.348^{\textdegree}C) }](https://tex.z-dn.net/?f=A_%7Bi%7D%20%3D%20%5Cfrac%7B489.795%5C%2CkW%7D%7B%280.63%5C%2C%5Cfrac%7BkW%7D%7Bm%5E%7B2%7D%5Ccdot%20%5E%7B%5Ctextdegree%7DC%7D%20%29%5Ccdot%2880.348%5E%7B%5Ctextdegree%7DC%29%20%7D)
![A_{i} = 9.676\,m^{2}](https://tex.z-dn.net/?f=A_%7Bi%7D%20%3D%209.676%5C%2Cm%5E%7B2%7D)
Length of a single pass counter flow heat exchanger is:
![L =\frac{A_{i}}{\pi\cdot D_{i}}](https://tex.z-dn.net/?f=L%20%3D%5Cfrac%7BA_%7Bi%7D%7D%7B%5Cpi%5Ccdot%20D_%7Bi%7D%7D)
![L = \frac{9.676\,m^{2}}{\pi\cdot (0.014\,m)}](https://tex.z-dn.net/?f=L%20%3D%20%5Cfrac%7B9.676%5C%2Cm%5E%7B2%7D%7D%7B%5Cpi%5Ccdot%20%280.014%5C%2Cm%29%7D)
![L = 220\,m](https://tex.z-dn.net/?f=L%20%3D%20220%5C%2Cm)
b) Given that tube wall is very thin, inner and outer heat transfer areas are similar and, consequently, the cold side heat transfer coefficient is approximately equal to the hot side heat transfer coefficient.
![U_{o} \approx 0.63\,\frac{kW}{m^{2}\cdot ^{\textdegree}C}](https://tex.z-dn.net/?f=U_%7Bo%7D%20%5Capprox%200.63%5C%2C%5Cfrac%7BkW%7D%7Bm%5E%7B2%7D%5Ccdot%20%5E%7B%5Ctextdegree%7DC%7D)
Answer:
lead dioxide,sulfate and lead acid
Answer:
sectores industriales, comerciales o públicos, o para el uso doméstico.
Explanation:
Team members and the work from ther