Published by:
CGP EDU Academic Team
Published on: September 12, 2026
In the water behind a high power dam (110 m high) the temperature difference between surface and bottom may be 10ºC. Compare the possible energy extraction from the thermal energy of a gram of water with that generated by allowing the water to flow over the dam through turbines in the conventional way.
Text Solution
Verified by ExpertsThe correct answer is:
B
Step 1: Calculate the gravitational potential energy (P.E) gained by 1 gram of water falling from a height of 110 m. The formula for potential energy is:
P.E = mgh
where:
m = mass = 1 gram = 0.001 kg
g = acceleration due to gravity ≈ 9.81 m/s²
h = height = 110 m
So,
P.E = 0.001 kg × 9.81 m/s² × 110 m = 1.0791 Joules.
Step 2: Calculate the energy extracted from the temperature difference of 10ºC. The specific heat capacity (C) of water is about 4.186 J/gºC.
The thermal energy (Q) can be calculated as:
Q = mCT
where:
C = specific heat capacity = 4.186 J/gºC
T = temperature difference = 10ºC
So,
Q = 1 g × 4.186 J/gºC × 10ºC = 41.86 Joules.
Step 3: Compare the two energies:
Gravitational Energy (P.E) = 1.0791 J
Thermal Energy (Q) = 41.86 J
The thermal energy extracted from the temperature difference is significantly greater than the potential energy from falling water. Thus, the energy extraction from thermal energy is more beneficial than from generating potential energy through gravity alone.
Therefore, the correct answer is B.
P.E = mgh
where:
m = mass = 1 gram = 0.001 kg
g = acceleration due to gravity ≈ 9.81 m/s²
h = height = 110 m
So,
P.E = 0.001 kg × 9.81 m/s² × 110 m = 1.0791 Joules.
Step 2: Calculate the energy extracted from the temperature difference of 10ºC. The specific heat capacity (C) of water is about 4.186 J/gºC.
The thermal energy (Q) can be calculated as:
Q = mCT
where:
C = specific heat capacity = 4.186 J/gºC
T = temperature difference = 10ºC
So,
Q = 1 g × 4.186 J/gºC × 10ºC = 41.86 Joules.
Step 3: Compare the two energies:
Gravitational Energy (P.E) = 1.0791 J
Thermal Energy (Q) = 41.86 J
The thermal energy extracted from the temperature difference is significantly greater than the potential energy from falling water. Thus, the energy extraction from thermal energy is more beneficial than from generating potential energy through gravity alone.
Therefore, the correct answer is B.
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