Published by:
CGP EDU Academic Team
Published on: September 12, 2026
Is the power of the Dneper hydroelectric station sufficient to raise the temperature of the water that passes through its turbines to boiling-point? The temperature of the water in the river is 20ºC.
Text Solution
Verified by ExpertsThe correct answer is:
B
To determine if the power of the Dneper hydroelectric station can raise the temperature of the water to boiling-point, we need to analyze the power output and the energy required to heat the water.
Step 1: Calculate the energy required to raise the temperature of the water.
The specific heat capacity of water is approximately 4.18 J/gºC. Assuming we want to raise the temperature from 20ºC to 100ºC (the boiling point), this is a temperature change of 80ºC.
Step 2: Use the formula for thermal energy:
\[ Q = mc\Delta T \]
where
m = mass of water (in grams),
c = specific heat capacity (4.18 J/gºC),
\Delta T = change in temperature (80ºC).
Therefore, for 1 kg of water (1000 g):
\[ Q = 1000 \times 4.18 \times 80 = 334400 J \]
Step 3: Determine the power output of the Dneper hydroelectric station (exact values needed). Assuming a power output of 100 MW (which is around the capacity), and using it over 1 second, the energy produced is 100,000,000 J. Since 334,400 J is much less than 100,000,000 J, it is sufficient.
Hence, the power of the Dneper hydroelectric station is indeed sufficient to raise the temperature of the water to boiling-point.
Step 1: Calculate the energy required to raise the temperature of the water.
The specific heat capacity of water is approximately 4.18 J/gºC. Assuming we want to raise the temperature from 20ºC to 100ºC (the boiling point), this is a temperature change of 80ºC.
Step 2: Use the formula for thermal energy:
\[ Q = mc\Delta T \]
where
m = mass of water (in grams),
c = specific heat capacity (4.18 J/gºC),
\Delta T = change in temperature (80ºC).
Therefore, for 1 kg of water (1000 g):
\[ Q = 1000 \times 4.18 \times 80 = 334400 J \]
Step 3: Determine the power output of the Dneper hydroelectric station (exact values needed). Assuming a power output of 100 MW (which is around the capacity), and using it over 1 second, the energy produced is 100,000,000 J. Since 334,400 J is much less than 100,000,000 J, it is sufficient.
Hence, the power of the Dneper hydroelectric station is indeed sufficient to raise the temperature of the water to boiling-point.
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