5-9 A 0.75-m³ rigid tank initially contains air whose den- sity is 1.18 kg/m³. The tank is connected to a high-pressure supply line through a valve. The valve is opened, and air is allowed to enter the tank until the density in the tank rises to 4.95 kg/m³. Determine the mass of air that has entered the tank.
5-9 A 0.75-m³ rigid tank initially contains air whose den- sity is 1.18 kg/m³. The tank is connected to a high-pressure supply line through a valve. The valve is opened, and air is allowed to enter the tank until the density in the tank rises to 4.95 kg/m³. Determine the mass of air that has entered the tank.
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
![**Problem 5-9:**
A 0.75-m³ rigid tank initially contains air whose density is 1.18 kg/m³. The tank is connected to a high-pressure supply line through a valve. The valve is opened, and air is allowed to enter the tank until the density in the tank rises to 4.95 kg/m³. Determine the mass of air that has entered the tank.
**Solution:**
1. **Initial Mass Calculation:**
\[
\text{Initial mass of air} = \text{Initial density} \times \text{Volume of tank} = 1.18 \, \text{kg/m}^3 \times 0.75 \, \text{m}^3 = 0.885 \, \text{kg}
\]
2. **Final Mass Calculation:**
\[
\text{Final mass of air} = \text{Final density} \times \text{Volume of tank} = 4.95 \, \text{kg/m}^3 \times 0.75 \, \text{m}^3 = 3.7125 \, \text{kg}
\]
3. **Mass of Air Entered:**
\[
\text{Mass entered} = \text{Final mass} - \text{Initial mass} = 3.7125 \, \text{kg} - 0.885 \, \text{kg} = 2.8275 \, \text{kg}
\]
**Conclusion:**
The mass of air that has entered the tank is 2.83 kg (rounded to two decimal places).
There are no additional graphs or diagrams in the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F353f4476-2375-44e0-a0df-7fa04e9ee69f%2Fd75c1ac8-daee-440e-b2cc-129958408feb%2F6972zw9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 5-9:**
A 0.75-m³ rigid tank initially contains air whose density is 1.18 kg/m³. The tank is connected to a high-pressure supply line through a valve. The valve is opened, and air is allowed to enter the tank until the density in the tank rises to 4.95 kg/m³. Determine the mass of air that has entered the tank.
**Solution:**
1. **Initial Mass Calculation:**
\[
\text{Initial mass of air} = \text{Initial density} \times \text{Volume of tank} = 1.18 \, \text{kg/m}^3 \times 0.75 \, \text{m}^3 = 0.885 \, \text{kg}
\]
2. **Final Mass Calculation:**
\[
\text{Final mass of air} = \text{Final density} \times \text{Volume of tank} = 4.95 \, \text{kg/m}^3 \times 0.75 \, \text{m}^3 = 3.7125 \, \text{kg}
\]
3. **Mass of Air Entered:**
\[
\text{Mass entered} = \text{Final mass} - \text{Initial mass} = 3.7125 \, \text{kg} - 0.885 \, \text{kg} = 2.8275 \, \text{kg}
\]
**Conclusion:**
The mass of air that has entered the tank is 2.83 kg (rounded to two decimal places).
There are no additional graphs or diagrams in the image.
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