Introduction:
The given figure is a volume versus temperature graph of two moles of helium gas. The question asks us to find the ratio of heat shown in the figure.

Explanation:
The ratio of heat shown in the figure can be found by using the First Law of Thermodynamics, which states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system:
ΔU = Q - W
where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system.

From the given graph, we can see that the volume of the gas increases as the temperature increases. This means that the gas is expanding and doing work on its surroundings.

Calculating work done:
The work done by the gas can be calculated using the equation:
W = - PΔV
where P is the pressure of the gas and ΔV is the change in volume.

From the graph, we can see that the pressure of the gas is constant. Therefore, the work done can be calculated as:
W = - PΔV = - 1 atm x 1 L = -1 L atm

Calculating change in internal energy:
The change in internal energy can be calculated using the equation:
ΔU = nCvΔT
where n is the number of moles of gas, Cv is the molar specific heat at constant volume, and ΔT is the change in temperature.

From the graph, we can see that the temperature of the gas increases from 300 K to 400 K. Therefore, the change in internal energy can be calculated as:
ΔU = nCvΔT = 2 mol x 3/2 R x (400 K - 300 K) = 300 R

Calculating heat added:
Using the First Law of Thermodynamics, we can rearrange the equation to solve for Q:
Q = ΔU + W

Substituting the values we calculated, we get:
Q = 300 R - 1 L atm

Calculating ratio of heat:
The ratio of heat shown in the figure can be found by comparing the areas under the curve. From the graph, we can see that the area under the curve for the process from A to B is greater than the area under the curve for the process from B to C. Therefore, the ratio of heat is greater for the process from A to B.

Conclusion:
The ratio of heat shown in the figure is greater for the process from A to B. The calculation involved using the First Law of Thermodynamics to calculate the work done, change in internal energy, and heat added to the system. The ratio of heat was then found by comparing the areas under the curve for the two processes.