Explanation:
The question gives $T$ in celsius. In kelvin, the temperature would be T+273.

Using the equation PV=nRT, we get number of moles = PV/RT. Since $M$ represents the number of moles, it will substitute into the equation for $n$ and $(T+273)$ will substitute as temperature in the equation giving

M=PV/R(T+273) which is answer A

Explanation:

The energy $E$ required to completely melt each substance is given by

• E=mL

where $m$ is the mass of the substance and $L$ is the specific latent heat of fusion.

Therefore, for a given power $P$, the duration tmelt of the plateau obeys the equation

tmelt=mL/P

The two substances have equal values of $m$ and $P$, meaning that since Substance $A$ has a higher tmelt value than Substance $B$, it also possesses a higher $L$ value. Hence, Statement III is incorrect.

The rates of temperature change before and after melting are related to the specific heat capacity $c$ via the expression

• E = mcΔT
• PΔt=mcΔT
• ΔTΔt=Pmc

The gradient of the graph is therefore inversely proportional to $c$.

In both solid and liquid state, Substance $A$ exhibits a higher value of ΔTΔt than Substance $B$, meaning that has a lower value of $c$. Hence, Statement I is correct.

Furthermore, for each substance, the gradient of the graph is lower in the liquid phase than in the solid phase, which means that after melting $c$ increases and Statement II is correct.

Explanation:
Due to the fixed volume, the separation between the gas molecules decreases. According to the ideal gas law, the pressure of the gas will increase and so does the collision frequency. The mass of the container will also be greater with the addition of more gas in the container. The only constant quantity is the average size of the molecules. It is dependent on molecular structure only. Therefore the answer is C.

Explanation:
To calculate $n$, the student would rearrange the formula to get

• n=PV/RT

In both operations, the percentage uncertainty must be added, therefore the correct answer is C (2 % + 6 % + 1 % = 9 %)

Explanation:

Solar constant (S) is the intensity of sun light at the orbit of the planet. For Earth, at a distance of 1AU from the sun, it is 1.36×10^3 W m^−2

Intensity is inversely proportional to the square of the distance from the source: I∝1/d^2

$\therefore$ Intensity at a distance 30 times as far will be 30^2 (=900) times weaker.

SNeptune=1360/900=1.5 W m^−2

Explanation:
Using V=W/q from the data booklet, we find that the charge q passing through the bulb in 2 seconds equals W/V=1000 J/200 V=5C.

Since I=Δq/Δt, the current in the bulb is 5C/2 s=2.5 A

Explanation:

Ice has half the specific heat capacity of liquid water and the rate of energy loss is constant. Therefore, after freezing the temperature of the system decreases at twice the rate compared to when cooling in the liquid state.

Explanation:

The kinetic model of ideal gases assumes that intermolecular forces (and therefore intermolecular potential energy) are negligible, and that the mean kinetic energy of molecules is directly proportional to gas temperature; hence, Properties I and II stay constant during the expansion. Conversely, Property III changes because gas pressure decreases during the expansion, and pressure scales with the frequency of molecular collisions with the walls of the piston.

Explanation:

The temperature of the solid is 373 $K$ (100 + 273) after the reaction takes place, so a temperature change of $(373-50)=323K$ is required to achieve the target temperature.

The energy $E$ needed for this change is related to the temperature change $\Delta T$ by the expression

E=mcΔT=323mc

Explanation:

From the circuit symbols in the data booklet, component A is a heating element.

When current flows in the circuit, the heating element will increase in temperature and the resistance will increase. This will increase the total resistance of the circuit and result in a decrease in the current due to the relationship I=V/R.

Explanation:
The average kinetic energy doubles which means that the temperature doubles. To maintain constant pressure, volume would have to double.

Since the number of molecules also doubles, volume would have to double again to maintain constant pressure.

Thus the volume must get 4 times larger from pV=nRT

I. Incorrect: As the heater heats both the water and the container, the container itself gains energy to increase temperature. Greater specific heat capacity means more energy is required to result in the same temperature change. So, for the glass container less energy is needed to reach 100oC which will take less time.

II. Correct: When there is isolation for the container there is less heat lost to the surroundings, resulting in higher efficiency. So the boiling finishes earlier.

III. Correct: As the amount of water increases more energy is required to result in same temperature change.

The change of state will occur at the same temperature as the original graph but take less time to complete.

Explanation:
I.  Chemical energy in fossil fuel is transformed into thermal energy by burning and thermal energy is used to move (kinetic energy) steam that rotates the turbine and generator (also kinetic energy). Finally, electric energy is produced in generators.

II.  The kinetic energy of wind rotates the blades (kinetic energy) and rotates the generator. Finally, electric energy is produced in a generators.

III.  The gravitational potential energy of water behind a dam converts into kinetic energy as water falls down and rotates the turbine and generator. Finally, electric energy is produced in generators.