Water flows at the rate of `0.1500 kg//min` through a tube and is heated by a heater dissipating `25.2W`. The inflow and outflow water temperatures are `15.2^@C` and `17.4^@C`, respectively. When the rate of flow is increased to `0.2318 kg//min` and the rate of heating to `37.8W`, the inflow and outflow temperature are unaltered. Find
i. the specific heat capacity of water
ii. the rate of loss of heat from the tube.

Explanation

To solve the problem step by step, we will break it down into two parts as requested: finding the specific heat capacity of water and calculating the rate of heat loss from the tube.

### Part i: Finding the Specific Heat Capacity of Water

1. **Identify Given Data:**
- Mass flow rate (initial) \( \dot{m}_1 = 0.1500 \, \text{kg/min} \)
- Power of heater \( P = 25.2 \, \text{W} \)
- Inflow temperature \( T_{in} = 15.2^\circ C \)
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