A `250cm^3` glass bottle is completely filled with water at `50^@C`. The bottle and water are heated to `60^@C`. How much water runs over if:
a. the expansion of the bottle is neglected:
b. the expansion of the bottle is included? Given the coefficient of areal expansion of glass `beta=1.2xx10^(-5)//K` and `gamma_("water")=60xx10^(-5)//^@C`.

Explanation

To solve the problem step by step, we will first address part (a) where the expansion of the bottle is neglected, and then we will move on to part (b) where the expansion of the bottle is included.

### Part (a): Expansion of the Bottle is Neglected

1. **Identify Initial Conditions**:
- Initial volume of water, \( V_0 = 250 \, \text{cm}^3 \)
- Initial temperature, \( T_1 = 50^\circ C \)
- Final temperature, \( T_2 = 60^\circ C \)
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