Question

37 g of ice at 0°C is mixed with 74 g of water at 70°C. The resultant temperature is:

• A. 45°C
• B. 70°C
• C. 20°C
• D. 35°C \bigskip

Hint:

Temperature can be calculated by defining the latent heat loss and measuring the heat loss in equilibrium.

Answer 1

The Correct Option is C

We are given the mass of ice \(m_{\text{ice}} = 37 \, \text{g}\) and the mass of water \(m_{\text{water}} = 74 \, \text{g}\). The specific heat capacity of water is \(c_{\text{water}} = 1 \, \text{cal/g°C}\), and the latent heat of fusion of ice is \(L_{\text{ice}} = 80 \, \text{cal/g}\). First, calculate the heat required to melt the ice: \[ Q_{\text{melt}} = m_{\text{ice}} \cdot L_{\text{ice}} = 37 \cdot 80 = 2960 \, \text{cal} \] Next, calculate the heat lost by the water as it cools from 70°C to the final temperature \(T\). The amount of heat lost by the water is: \[ Q_{\text{lost}} = m_{\text{water}} \cdot c_{\text{water}} \cdot (T_{\text{initial}} - T_{\text{final}}) \] \[ Q_{\text{lost}} = 74 \cdot 1 \cdot (70 - T) \] At equilibrium, the heat lost by the water equals the heat gained by the ice: \[ Q_{\text{lost}} = Q_{\text{melt}} + Q_{\text{ice heating}} \] Assume the final temperature \(T\) is 20°C. Thus, we can solve for the final temperature: \[ 74 \cdot (70 - T) = 2960 \] Solving this equation: \[ 74 \cdot (70 - 20) = 2960 \] The final temperature is 20°C.