Question

Komal likes to have a tepid bath. She has 5 kg of water at 25 (degree Celcius). How many kg of water should she boil to have a comfortable bath of 45 (degree Celcius)?

Answer 1

Komal likes to have a tepid bath. She has 5 kg of water at 25 (degree Celcius). How many kg of water should she boil to have a comfortable bath of 45 (degree Celcius)?

Solution:

Let:

$$m _ {1} = 5 \, \text{kg}$$ $$T _ {1} = 25{}^{\circ} \text{C}$$ $$T _ {2} = 100{}^{\circ} \text{C} \quad \text{the temperature of boiling water}$$ $$T _ {3} = 45{}^{\circ} \text{C}$$

$m _ {2} - ?$

According to the laws of thermodynamics:

$$Q _ {1} + Q _ {2} = Q _ {3}$$ $$m _ {1} c T _ {1} + m _ {2} c T _ {2} = (m _ {1} + m _ {2}) c T _ {3}$$ $$m _ {1} T _ {1} + m _ {2} T _ {2} = m _ {1} T _ {3} + m _ {2} T _ {3}$$ $$m _ {2} (T _ {2} - T _ {3}) = m _ {1} T _ {3} - m _ {1} T _ {1}$$ $$m _ {2} = \frac {m _ {1} T _ {3} - m _ {1} T _ {1}}{T _ {2} - T _ {3}}$$ $$m _ {2} = \frac {5 \cdot 45 - 5 \cdot 25}{100 - 45} = 1.82 \, \text{kg}$$

Answer: 1.82 kg