Introduction:
In this question, we are given the pressure of air in a constant volume air thermometer at two different temperatures (0°C and 100°C). We need to determine the coefficient of cubical expansion of air.

Given:
Pressure at 0°C (P1) = 0.8 atm
Pressure at 100°C (P2) = 1.093 atm

Formula:
The coefficient of cubical expansion (α) is given by the equation:
α = (1/V) * (dV/dT)
where,
V is the volume of the gas
dT is the change in temperature

Solution:
To determine the coefficient of cubical expansion, we can use the ideal gas law equation:
PV = nRT
where,
P is the pressure
V is the volume
n is the number of moles of gas
R is the ideal gas constant
T is the temperature

Step 1: Calculate the number of moles of gas:
Since the volume is constant, the number of moles of gas will also be constant. Therefore, we can write the equation as:
P1V = nRT1
P2V = nRT2

Step 2: Calculate the change in temperature:
The change in temperature is given by:
ΔT = T2 - T1

Step 3: Calculate the change in volume:
Using the ideal gas law equation, we can write:
P1V = nRT1
P2V = nRT2

Dividing these two equations, we get:
V2/V1 = T2/T1
V2 = V1 * (T2/T1)

Therefore, the change in volume is given by:
ΔV = V2 - V1 = V1 * (T2/T1) - V1 = V1 * (T2/T1 - 1)

Step 4: Calculate the coefficient of cubical expansion:
Using the formula for the coefficient of cubical expansion, we have:
α = (1/V) * (dV/dT) = (1/V1) * (ΔV/ΔT)

Substituting the values, we get:
α = (1/V1) * (V1 * (T2/T1 - 1) / (T2 - T1))

Simplifying, we get:
α = (T2 - T1) / (T1 * (T2 - T1))
α = 1 / T1

Therefore, the coefficient of cubical expansion of air is 1 / T1.

Conclusion:
The coefficient of cubical expansion of air is given by the equation α = 1 / T1, where T1 is the initial temperature. In this question, the initial temperature is 0°C, so the coefficient of cubical expansion of air is 1 / 0 = Infinity.