A rigid tank contains 25 kg of saturated liquid water at 90°C. What will be the volume of the tank? [Given : Specific volume of saturated liquid at 90°C = 0.00104 m3/kg .]
26 litre
In this problem, we need to determine the volume of a rigid tank containing a specific amount of saturated liquid water at a given temperature. We are provided with the mass of the water and its specific volume at that temperature. Understanding the relationship between mass, volume, and specific volume is crucial for solving this problem.
Specific Volume Concept
Specific volume is an intensive property of a substance, defined as the volume occupied by a unit mass of that substance. It is the reciprocal of density. For fluids like water, specific volume changes with temperature and pressure. In this case, we are given the specific volume of saturated liquid water at 90°C, denoted as \(v_f\).
- Specific volume (\(v\)) is measured in units like cubic meters per kilogram (\(\text{m}^3/\text{kg}\)) or cubic feet per pound-mass (\(\text{ft}^3/\text{lbm}\)).
- It helps us relate the total volume of a substance to its total mass.
Tank Volume Calculation
To find the total volume of the rigid tank, we can use the fundamental relationship that connects mass, specific volume, and total volume. The total volume (\(V\)) of a substance is obtained by multiplying its mass (\(m\)) by its specific volume (\(v\)).
Given Parameters:
- Mass of saturated liquid water (\(m\)) = 25 kg
- Specific volume of saturated liquid water at 90°C (\(v_f\)) = 0.00104 \(\text{m}^3/\text{kg}\)
Formula for Volume:
The formula to calculate the volume of the tank is:
\( V = m \times v_f \)
Where:
- \(V\) = Total volume of the tank
- \(m\) = Mass of the substance
- \(v_f\) = Specific volume of the saturated liquid
Step-by-Step Calculation:
Let's substitute the given values into the formula:
\( V = 25 \, \text{kg} \times 0.00104 \, \text{m}^3/\text{kg} \)
Performing the multiplication:
\( V = 0.026 \, \text{m}^3 \)
Converting Volume Units
The calculated volume is in cubic meters (\(\text{m}^3\)). The options are given in litres and cubic meters. Since one of the options is in litres, we should convert the calculated volume from \(\text{m}^3\) to litres.
We know that:
\( 1 \, \text{m}^3 = 1000 \, \text{litres} \)
Now, convert \(0.026 \, \text{m}^3\) to litres:
\( V_{\text{litres}} = 0.026 \, \text{m}^3 \times 1000 \, \text{litres/m}^3 \)
\( V_{\text{litres}} = 26 \, \text{litres} \)
Final Tank Volume
Based on our calculations, the volume of the rigid tank is 26 litres.
| Parameter | Value | Unit |
|---|---|---|
| Mass (\(m\)) | 25 | kg |
| Specific Volume (\(v_f\)) | 0.00104 | m\(^3\)/kg |
| Calculated Volume (\(V\)) | 0.026 | m\(^3\) |
| Converted Volume (\(V_{\text{litres}}\)) | 26 | litres |
Important Questions from Phase Change of a Pure Substance
- Which of the following exists in a P-V diagram for water?
What the region (2) in the p-V diagram given below is called?
The saturation temperature of steam with increase in pressure increases _________.
A rigid tank contains 10 kg of water at 90°C. If 8 kg of water is in liquid form and the rest is in vapour form, what will be the volume of the tank?
[Given: At 90°C, saturation pressure is 70 kPa , specific volume at saturated liquid state = 0.001 m3/kg , specific volume at saturated vapour state = 2.36 m3/kg.]
- The triple point on a T-s diagram is _________.
