Total heat=40×0.075=3 cal=CV
Cp-Cv=R
Cp=3+2=5
Cp/CV=5/3
hence it is monoatomic.

**Atomicity of a Gas**

The atomicity of a gas refers to the number of atoms present in one molecule of the gas. It can be determined by analyzing the specific heat of the gas at constant volume. Specific heat is the amount of heat energy required to raise the temperature of a substance by 1 degree Celsius or 1 Kelvin.

**Specific Heat and Atomicity**

The specific heat of a gas at constant volume is directly related to its atomicity. The formula to calculate the specific heat at constant volume (Cv) is:

Cv = (f/2) * R

Where:
Cv = specific heat at constant volume,
f = degree of freedom,
R = gas constant (8.314 J/mol·K).

In this case, the specific heat of the gas is given as 0.075 calories. To convert calories to joules, we need to multiply by 4.184:

0.075 calories * 4.184 J/calorie = 0.3138 J

Now we can rearrange the equation to solve for the degree of freedom (f):

f = (2 * Cv) / R

Substituting the values:

f = (2 * 0.3138 J) / 8.314 J/mol·K
f ≈ 0.075

Since the degree of freedom corresponds to the number of atoms in the molecule minus one, we can say that the atomicity of the gas is:

Atomicity = degree of freedom + 1
Atomicity = 0.075 + 1
Atomicity ≈ 1.075

Therefore, the atomicity of the gas is approximately 1.075.

**Conclusion**

The atomicity of a gas can be determined by analyzing its specific heat at constant volume. By using the formula for specific heat and rearranging the equation, we can calculate the degree of freedom, which is directly related to the atomicity. In this case, the specific heat of the gas was given as 0.075 calories, and the resulting atomicity was approximately 1.075.