Introduction:
The elasticity of a gas refers to its ability to change its volume in response to changes in pressure or temperature. Two important types of elasticity in gases are adiabatic elasticity and isothermal elasticity. Adiabatic elasticity is the ability of a gas to change its volume without any exchange of heat with the surroundings, whereas isothermal elasticity is the ability of a gas to change its volume while maintaining a constant temperature.

Formula:
The ratio of adiabatic elasticity (Eadiabatic) to isothermal elasticity (Eisothermal) can be determined using the following formula:

Eadiabatic/Eisothermal = γ

where γ is the adiabatic index or heat capacity ratio. For a diatomic gas, γ is equal to 7/5 or approximately 1.4.

Calculation:
To find the ratio of adiabatic to isothermal elasticity, we can substitute the value of γ into the formula:

Eadiabatic/Eisothermal = 1.4

Therefore, the correct answer is B) 1.4.

Explanation:
The adiabatic process involves the compression or expansion of a gas without any exchange of heat with the surroundings. In this process, the temperature of the gas changes due to the work done on or by the gas. The change in volume is greater for adiabatic elasticity compared to isothermal elasticity, as the gas experiences a larger change in temperature.

On the other hand, the isothermal process involves the compression or expansion of a gas while maintaining a constant temperature. In this process, the heat exchanged with the surroundings compensates for the work done on or by the gas, resulting in a constant temperature. The change in volume is smaller for isothermal elasticity compared to adiabatic elasticity, as the gas does not experience a significant change in temperature.

Therefore, the ratio of adiabatic to isothermal elasticity for a diatomic gas is approximately 1.4, as determined by the adiabatic index or heat capacity ratio (γ) of 7/5.

Ratio of adiabatic to isothermal elasticity=γ
=Cp/Cv=7/5=1.4