Answer:
a. 164 °F b. 91.11 °C c. 1439.54 kJ
Explanation:
a. [1 pts] How many degrees Fahrenheit (°F) must you raise the temperature?
Since the starting temperature is 48°F and the final temperature which water boils is 212°F, the number of degrees Fahrenheit we would need to raise the temperature is the difference between the final temperature and the initial temperature.
So, Δ°F = 212 °F - 48 °F = 164 °F
b. [2 pts] How many degrees Celsius (°C) must you raise the temperature?
To find the degree change in Celsius, we convert the initial and final temperature to Celsius.
°C = 5(°F - 32)/9
So, 48 °F in Celsius is
°C₁ = 5(48 - 32)/9
°C₁ = 5(16)/9
°C₁ = 80/9
°C₁ = 8.89 °C
Also, 212 °F in Celsius is
°C₂ = 5(212 - 32)/9
°C₂ = 5(180)/9
°C₂ = 5(20)
°C₂ = 100 °C
So, the number of degrees in Celsius you must raise the temperature is the temperature difference between the final and initial temperatures in Celsius.
So, Δ°C = °C₂ - °C₁ = 100 °C - 8.89 °C = 91.11 °C
c. [2 pts] How much energy is required to heat the four quarts of water from
48°F to 212°F (boiling)?
Since we require 15.8 kJ for every degree Celsius of temperature increase of the four quarts of water, that is 15.8 kJ/°C and it rises by 91.11 °C, then the amount of energy Q required is Q = amount of heat per temperature rise × temperature rise = 15.8 kJ/°C × 91.11 °C = 1439.54 kJ
Answer:
![\dot W_{out} = 3374.289\,\frac{BTU}{s}](https://tex.z-dn.net/?f=%5Cdot%20W_%7Bout%7D%20%3D%203374.289%5C%2C%5Cfrac%7BBTU%7D%7Bs%7D)
Explanation:
The model for the turbine is given by the First Law of Thermodynamics:
![- \dot W_{out} + \dot m \cdot (h_{in} - h_{out}) = 0](https://tex.z-dn.net/?f=-%20%5Cdot%20W_%7Bout%7D%20%2B%20%5Cdot%20m%20%5Ccdot%20%28h_%7Bin%7D%20-%20h_%7Bout%7D%29%20%3D%200)
The turbine power output is:
![\dot W_{out} = \dot m\cdot (h_{in}-h_{out})](https://tex.z-dn.net/?f=%5Cdot%20W_%7Bout%7D%20%3D%20%5Cdot%20m%5Ccdot%20%28h_%7Bin%7D-h_%7Bout%7D%29)
The volumetric flow is:
![\dot V = \frac{\pi}{4} \cdot \left( \frac{2}{12}\,ft \right)^{2}\cdot (620\,\frac{ft}{s} )](https://tex.z-dn.net/?f=%5Cdot%20V%20%3D%20%5Cfrac%7B%5Cpi%7D%7B4%7D%20%5Ccdot%20%5Cleft%28%20%5Cfrac%7B2%7D%7B12%7D%5C%2Cft%20%5Cright%29%5E%7B2%7D%5Ccdot%20%28620%5C%2C%5Cfrac%7Bft%7D%7Bs%7D%20%29)
![\dot V \approx 13.526\,\frac{ft^{3}}{s}](https://tex.z-dn.net/?f=%5Cdot%20V%20%5Capprox%2013.526%5C%2C%5Cfrac%7Bft%5E%7B3%7D%7D%7Bs%7D)
The specific volume of steam at inlet is:
State 1 (Superheated Steam)
![\nu = 1.33490\,\frac{ft^{3}}{lbm}](https://tex.z-dn.net/?f=%5Cnu%20%3D%201.33490%5C%2C%5Cfrac%7Bft%5E%7B3%7D%7D%7Blbm%7D)
The mass flow is:
![\dot m = \frac{\dot V}{\nu}](https://tex.z-dn.net/?f=%5Cdot%20m%20%3D%20%5Cfrac%7B%5Cdot%20V%7D%7B%5Cnu%7D)
![\dot m = \frac{13.526\,\frac{ft^{3}}{s} }{1.33490\,\frac{ft^{3}}{lbm} }](https://tex.z-dn.net/?f=%5Cdot%20m%20%3D%20%5Cfrac%7B13.526%5C%2C%5Cfrac%7Bft%5E%7B3%7D%7D%7Bs%7D%20%7D%7B1.33490%5C%2C%5Cfrac%7Bft%5E%7B3%7D%7D%7Blbm%7D%20%7D)
![\dot m = 10.133\,\frac{lbm}{s}](https://tex.z-dn.net/?f=%5Cdot%20m%20%3D%2010.133%5C%2C%5Cfrac%7Blbm%7D%7Bs%7D)
Specific enthalpies at inlet and outlet are, respectively:
State 1 (Superheated Steam)
![h = 1479.74\,\frac{BTU}{lbm}](https://tex.z-dn.net/?f=h%20%3D%201479.74%5C%2C%5Cfrac%7BBTU%7D%7Blbm%7D)
State 2 (Saturated Vapor)
![h = 1146.1\,\frac{BTU}{lbm}](https://tex.z-dn.net/?f=h%20%3D%201146.1%5C%2C%5Cfrac%7BBTU%7D%7Blbm%7D)
The turbine power output is:
![\dot W_{out} = (10.133\,\frac{lbm}{s} )\cdot (1479.1\,\frac{BTU}{lbm}-1146.1\,\frac{BTU}{lbm})](https://tex.z-dn.net/?f=%5Cdot%20W_%7Bout%7D%20%3D%20%2810.133%5C%2C%5Cfrac%7Blbm%7D%7Bs%7D%20%29%5Ccdot%20%281479.1%5C%2C%5Cfrac%7BBTU%7D%7Blbm%7D-1146.1%5C%2C%5Cfrac%7BBTU%7D%7Blbm%7D%29)
![\dot W_{out} = 3374.289\,\frac{BTU}{s}](https://tex.z-dn.net/?f=%5Cdot%20W_%7Bout%7D%20%3D%203374.289%5C%2C%5Cfrac%7BBTU%7D%7Bs%7D)
Answer:
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Explanation:
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