A vessel of volume $$\,\,1.0\,\,{m^3}$$ contains a mixture of liquid water and steam in equilibrium at $$1.0$$ bar.Given that $$90\% $$ of the volume is occupied by the steam, find the dryness fraction of the mixture. Assume, at $$1.0$$ bar, $${\,{v_f} = 0.001\,\,{m^3}/kg}$$ and $${\,{v_g} = 1.7\,\,{m^3}/kg}.$$

In the vicinity of the triple point, the vapour pressures of liquid and solid ammonia are respectively given by
$$\eqalign{ & \ln \,\,P = 15.16 - 3063/T \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,and \cr & \ln \,\,P = 18.70 - 3754/T \cr} $$

Where $$p$$ is in atmospheres and $$T$$ is in Kelvin. What is the temperature at the triple point.