Q76: Find the mass of ice required to lower the temperature... - Dairy and Food Engineering-I - Dairy Engineering- ICAR JRF/SRF 2024 | Agrigyan

• Thermal Energy Balance for Ice Melting:
• Sensible Heat Released by Cooling Water ($20^\circ\text{C} \rightarrow 0^\circ\text{C}$):

$$Q_{\text{released}} = m_w \times C_w \times \Delta T = 500\text{ g} \times 4.2\text{ J/(g}\cdot^\circ\text{C)} \times (20 - 0)^\circ\text{C} = 42,000\text{ J}$$

• Latent Heat Absorbed by Melting Ice ($0^\circ\text{C}$ ice $\rightarrow 0^\circ\text{C}$ water):

$$Q_{\text{absorbed}} = m_i \times L_f = m_i \times 336\text{ J/g}$$

• Conservation of Energy:

$$m_i \times 336 = 42,000 \implies m_i = \frac{42,000}{336} = 125\text{ g}$$

• Conclusion: 125 g (Option 2).

Correct option: (2) 1259