According to Charles's law, the volume of a gas is directly proportional to its temperature, when pressure is held constant. Mathematically, this can be expressed as:

```

V1/T1 = V2/T2

```

Where V1 and T1 represent the initial volume and temperature, respectively, and V2 and T2 represent the final volume and temperature. Given that the volume remains constant and pressure changes we can represent the relationship as,

```

P1/T1 = P2/T2

```

Where P1 and T1 represent the initial pressure and temperature, respectively, and P2 and T2 represent the final pressure and temperature.

Rearranging the equation to solve for T2, we have:

```

T2 = (P2 * T1) / P1

```

Substituting the given values:

```

T2 = (900 mmHg * 10.0 C) / 700 mmHg

```

```

T2 = 12.9 C

```

Therefore, the new temperature is 12.9 C.