Heat is a form of energy resulting from molecular velocity. Temperature is a scale to measure the amount of internal energy stored as heat, known as enthalpy. Entropy is the relative disorder of a system.

In order for a heat transfer to occur, the system must not be in equilibrium. In other words, there must be a difference in heat energy between two regions of the system, which will allow heat energy to travel from the region of high energy to the region of low energy. This condition is easily identified by a temperature gradient, in which heat will from the region of high temperature to the region of low temperature until the system is at an equilibrium temperature.

This question asks about the zeroth law of thermodynamics which states if two systems are in thermal equilibrium with another system, then all three systems will be in thermal equilibrium with each other.

The other answer choices in this question talk about the other three laws of thermodynamics. First law of thermodynamics states that energy of the universe is constant and that energy cannot be created or destroyed. The second law states that the entropy of the universe is constantly increasing, even if local entropy decreases. The third law states that a pure crystal at absolute zero  has zero entropy.

The Second Law of Thermodynamics states that entropy of the universe always increases. The loss of heat energy to the lake due to friction leads to an increase in the entropy of the universe, and thus the return of that energy to move the child would lead to a decrease in the entropy of the universe.

Nevertheless, the hypothetical movement of the child with this energy is allowed by the First Law of Thermodynamics.

The Gibbs Free Energy equation makes use of clearly delineated systems and surroundings.  In this example, the water is freezing or melting depending on conditions. This is accompanied by thermal exchanges with other players, such as the snow and stove. Thus, the water is the system, and everything else (technically, everything else in the universe) comprises the surroundings. 

Given the fact that combustion reactions are exothermic, you should expect the heat of reaction to be negative (ruling out two answer choices). The heat of reaction is equal to the heat of formation of the products minus the heat of formation of the reactants. Be sure to refer to the balanced equation for the correct number of moles for each compound.

Oxygen is not included, as it is in elemental form and therefore has a heat of formation equal to zero.

To calculate the , the following formula is used. Remember that the coefficients of the balanced chemical equation must be included, as shown. Also, recall that the  of any pure element is zero.

Now we can plug in the given values and solve for the enthalpy of reaction.

To turn the water into steam, the stove must first raise the temperature of the water, and then provide energy to change the phase. This requires two distinct steps.

Find the energy to raise the temperature of the water using the equation . We know our mass, the specific heat of water, and the change in temperature. Use the given values to find the necessary heat.

Now, we need to find the energy needed to convert the water to a gas. We will use the equation .

Finally, we add the energy for the two steps to find the total energy required.

Basically, this is a unit conversion problem. Starting with grams of sulfur, convert to moles of sulfur, and finally to kJ of heat released. Note that the given enthalpy of reaction, , is the amount of heat released when two moles of sulfur react with three moles of oxygen.

Note that a negative enthalpy of reaction means the process is exothermic and releases heat, while a positive enthalpy of reaction would mean the process is endothermic and absorbs heat.

Since the system is isolated, the amount of heat transferred away from the unknown substance must equal the heat transferred to the water. To calculate these heats, use 

For the water, .

For the unknown substance, 

Set these values equal to get c_x = 2.39 J/g^oC, approximately 2.4 J/g^oC.

There are three distinct steps in this transformation: 1) heating the ice from -30^oC to 0^oC, 2) melting the ice at 0^oC, and 3) heating the water from 0^oC to 40^oC.

When there is a temperature change, we use , and when there is melting or freezing, we use .

1) 

2) 

3) 

Adding these three pieces together gives the total enthalpy change, which is equal to change in energy.