We could (a) stir faster and (b) warm the mixture.
<em>Stirring faster</em> moves freshly-dissolved sugar away from the solid and allows new water molecules to contact with the surface,
<em>Warming the mixture</em> gives the water molecules more kinetic energy, so their collisions with the surface of the sugar will be more effective in removing the sugar molecules.
A. The box will move to the right
Heat energy is calculated by multiplying the mass, specific heat capacity of a substance by the change in temperatures. Therefore,the heat lost by water will be given by mass of water (in kg) × specific heat capacity of water × change in temperature. This heat will be equivalent to the heat gained by the spoon calculated by mass of the spoon by specific heat capacity by change in temperature. (considering that the specific heat capacity of gold is 125.6 J/kg/k)
hence, 0.05 kg × 49 × 125.6 J/kg/k = 307.72 Joules
therefore, heat lost by water is equivalent to 307.72 Joules