VIPSolutionsAct like a helpful tutor and exlain me : Give step-by-step solution with explanation and final answer: Give detailed answer in englishQuestion 3 Usted es considerado para que determine la irreversiblidad para un compresor adiabatico de 300 hp que aumenta la presion de entrada 10 veces. La temperatura ambiental considerada es de 66 Fahrenheit y la del contorno del compresor se considera de 51 Fahrenheit. Dado que las entropias absolutas son: s1=0.1982 Btu/(lbm R); 52 = 0.3303 Btu/(lbm R) para un flujo de masa de 27 pps y la constante del gas es de R= 44.02 Ibf ft/(Ibm R). Ingrese la irreversibilidad o exergia destruida en hp. No ingrese las unidades e ingrese tres valores decimales.
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Question 3
Usted es considerado para que determine la irreversiblidad para un compresor adiabatico de 300 hp que aumenta la presion de
entrada 10 veces.
La temperatura ambiental considerada es de 66 Fahrenheit y la del contorno del compresor se considera de 51 Fahrenheit.
Dado que las entropias absolutas son: s1=0.1982 Btu/(lbm R); 52 = 0.3303 Btu/(lbm R) para un flujo de masa de 27 pps y la
constante del gas es de R= 44.02 Ibf ft/(Ibm R).
Ingrese la irreversibilidad o exergia destruida en hp. No ingrese las unidades e ingrese tres valores decimales.
This is AI generated Response.
Asked by: manish kumar
Created at: 2025-10-12 10:08:21
Asked by: manish kumar
Created at: 2025-10-12 10:08:21
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## Step-by-Step Solution
Let's solve for the **irreversibility (exergy destroyed)** in an adiabatic compressor.
### **Given Data**
- Compressor Power, \( W = 300 \) hp
- Pressure increases by 10x (not needed directly for exergy destroyed with given entropies)
- Ambient temperature \( T_ = 66^\circ F \)
- Compressor surroundings \( T_{surr} = 51^\circ F \)
- Entropies: \( s_1 = .1982 \) Btu/(lbm·R), \( s_2 = .3303 \) Btu/(lbm·R)
- Mass flow rate, \( \dot{m} = 27 \) lbm/s
- Gas constant, \( R = 44.02 \) lbf·ft/(lbm·R)
- **Required:** Find irreversibility/exergy destroyed (\( I \)) in **hp** (do not include units in answer).
---
### **Step 1: Convert Temperatures to Rankine**
Fahrenheit to Rankine:
\[
T(R) = T(^\circ F) + 459.67
\]
- \( T_ = 66 + 459.67 = 525.67 \) R
- \( T_{surr} = 51 + 459.67 = 510.67 \) R
But for exergy destroyed, use the ambient temperature (\( T_ \)).
---
### **Step 2: Find Entropy Generation (\( \Delta s_{gen} \))**
\[
\Delta s_{gen} = s_2 - s_1
\]
\[
\Delta s_{gen} = .3303 - .1982 = .1321~\text{Btu/(lbm·R)}
\]
---
### **Step 3: Calculate Exergy Destroyed (\( \dot{I} \))**
Irreversibility (exergy destroyed) rate:
\[
\dot{I} = T_ \cdot \dot{m} \cdot \Delta s_{gen}
\]
Where:
- \( T_ \): in Rankine
- \( \dot{m} \): in lbm/s
- \( \Delta s_{gen} \): in Btu/(lbm·R)
\[
\dot{I} = 525.67~\text{R} \times 27~\text{lbm/s} \times .1321~\frac{\text{Btu}}{\text{lbm}\cdot\text{R}}
\]
Calculate:
\[
27 \times .1321 = 3.5667
\]
\[
\dot{I} = 525.67 \times 3.5667 = 1,874.697~\text{Btu/s}
\]
---
### **Step 4: Convert Btu/s to hp**
1 hp = 2545 Btu/hr
First, convert Btu/s to Btu/hr:
\[
1,874.697~\text{Btu/s} \times 360~\text{s/hr} = 6,749,909.2~\text{Btu/hr}
\]
Now, convert to hp:
\[
\text{Exergy destroyed (hp)} = \frac{6,749,909.2}{2545} = 2,652.41~\text{hp}
\]
---
### **Step 5: Final Answer**
**Enter only three decimal places as requested:**
\[
\boxed{2652.409}
\]
---
## **Summary Table**
| Step | Value |
|-----------------------------|-------------|
| \( \Delta s_{gen} \) | .1321 Btu/(lbm·R) |
| Exergy destroyed (\( \dot{I} \)), Btu/s | 1874.697 |
| Exergy destroyed, hp | 2652.409 |
---
## **Final Answer (rounded to three decimals)**
> **2652.409**
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