The 50 MWe Andasol solar thermal power plant in Spain uses two tanks of molten salt (specific heat c= 1.47 kJ/kg °C), each storing 28,000 tonne. The salt is heated from 293°C to 550°C. How much energy is stored in each tank? В. A. If the efficiency is 16%, how long can the plant operate to produce 50 MW.?
The 50 MWe Andasol solar thermal power plant in Spain uses two tanks of molten salt (specific heat c= 1.47 kJ/kg °C), each storing 28,000 tonne. The salt is heated from 293°C to 550°C. How much energy is stored in each tank? В. A. If the efficiency is 16%, how long can the plant operate to produce 50 MW.?
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![**Problem 9.8**
The 50 MW\(_e\) Andasol solar thermal power plant in Spain uses two tanks of molten salt (specific heat \( c = 1.47 \text{ kJ/kg} \cdot °C \)), each storing 28,000 tonnes. The salt is heated from 293°C to 550°C.
**A. How much energy is stored in each tank?**
**B. If the efficiency is 16%, how long can the plant operate to produce 50 MW?**
---
### Detailed Analysis
**A. Calculating Energy Stored in Each Tank**
To find the total energy stored in each tank, we use the formula for heat energy:
\[ Q = mc\Delta T \]
where:
- \( Q \) is the heat energy stored (in kJ),
- \( m \) is the mass of the molten salt (in kg),
- \( c \) is the specific heat capacity (in kJ/kg°C),
- \( \Delta T \) is the change in temperature (in °C).
Given:
- Mass \( m \) = 28,000 tonnes = 28,000,000 kg
- Specific heat capacity \( c \) = 1.47 kJ/kg°C
- Temperature change \( \Delta T \) = 550°C - 293°C = 257°C
Substitute the values into the formula:
\[ Q = 28,000,000 \, \text{kg} \times 1.47 \, \text{kJ/kg} \cdot °C \times 257 \, °C \]
\[ Q = 10,580,400,000 \, \text{kJ} \]
So, the energy stored in each tank is 10,580,400,000 kJ.
**B. Operating Time to Produce 50 MW**
To produce 50 MW with an efficiency of 16%, we need to find the useful energy produced by each tank and then determine how long the tank can produce electricity.
First, calculate the useful energy (in kJ) that can be extracted at 16% efficiency:
\[ \text{Useful Energy} = Q \times \text{Efficiency} \]
\[ \text{Useful Energy} = 10,580,400,000 \, \text{kJ} \times 0.16 \]
\[ \text{Useful Energy} =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf192c4a-3623-40a7-8b1d-18d623c8a61a%2F7672ad70-670d-4aa1-87ed-03b160753f1c%2Fwb4wu7g_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 9.8**
The 50 MW\(_e\) Andasol solar thermal power plant in Spain uses two tanks of molten salt (specific heat \( c = 1.47 \text{ kJ/kg} \cdot °C \)), each storing 28,000 tonnes. The salt is heated from 293°C to 550°C.
**A. How much energy is stored in each tank?**
**B. If the efficiency is 16%, how long can the plant operate to produce 50 MW?**
---
### Detailed Analysis
**A. Calculating Energy Stored in Each Tank**
To find the total energy stored in each tank, we use the formula for heat energy:
\[ Q = mc\Delta T \]
where:
- \( Q \) is the heat energy stored (in kJ),
- \( m \) is the mass of the molten salt (in kg),
- \( c \) is the specific heat capacity (in kJ/kg°C),
- \( \Delta T \) is the change in temperature (in °C).
Given:
- Mass \( m \) = 28,000 tonnes = 28,000,000 kg
- Specific heat capacity \( c \) = 1.47 kJ/kg°C
- Temperature change \( \Delta T \) = 550°C - 293°C = 257°C
Substitute the values into the formula:
\[ Q = 28,000,000 \, \text{kg} \times 1.47 \, \text{kJ/kg} \cdot °C \times 257 \, °C \]
\[ Q = 10,580,400,000 \, \text{kJ} \]
So, the energy stored in each tank is 10,580,400,000 kJ.
**B. Operating Time to Produce 50 MW**
To produce 50 MW with an efficiency of 16%, we need to find the useful energy produced by each tank and then determine how long the tank can produce electricity.
First, calculate the useful energy (in kJ) that can be extracted at 16% efficiency:
\[ \text{Useful Energy} = Q \times \text{Efficiency} \]
\[ \text{Useful Energy} = 10,580,400,000 \, \text{kJ} \times 0.16 \]
\[ \text{Useful Energy} =
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