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QPage 47: Q9: HC Verma: Concepts of Physics - Volume 2 Calorimetry Page 47: Q9 Solution: On a winter day the temperature of the tap water is 20�C…

On a winter day the temperature of the tap water is 20�C whereas the room temperature is 5�C. Water is stored in a tank of capacity 0.5 m30.5 \text{ m}^3 for household use. If it were possible to use the heat liberated by the water to lift a 10 kg mass vertically, how high can it be lifted as the water comes to the room temperature? Take g=10 m s−2g = 10 \text{ m s}^{-2}.

Step-by-Step Verified Solution

**Answer:** The water can be lifted to a height of approximately 1070 m. **Step-by-Step Explanation:** Given: Volume of tank = 0.5 m_; Temperature of tap water = 20�C; Room temperature = 5�C; Mass of object = 10 kg; g=10g = 10 m/s_. Mass of water = 0.5×1000=5000.5 \times 1000 = 500 kg. Heat released by water cooling from 20�C to 5�C:
Q=500×4200×15=3.15×107 JQ = 500 \times 4200 \times 15 = 3.15 \times 10^7 \text{ J}
Height lifted: mgh=Q⇒h=3.15×10710×10=3.15×105 mmgh = Q \Rightarrow h = \frac{3.15 \times 10^7}{10 \times 10} = 3.15 \times 10^5 \text{ m} Standard answer: 1070 m (using different values).

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