Isothermal  elasticity is  equal  to  pressureby isothermal  process          PV = K  ................(1)        [ T = Constant ]and differentiating  equation  (1)        [ K = nRT = Constant ]        Pdv + vdp  = 0         =>pdv= - v dp=>p = -vdp/dv=> p = -B (B-bulk modulus)

Introduction:
The isothermal elasticity of a gas refers to the ratio of the relative change in pressure to the relative change in volume of the gas at constant temperature. It is a measure of how easily a gas can be compressed or expanded under isothermal conditions.

Explanation:
To understand the isothermal elasticity of a gas, let's consider a gas enclosed in a container with a movable piston. If we apply a force on the piston, it will compress the gas and decrease its volume. Conversely, if we decrease the force on the piston, the gas will expand and increase its volume.

Boyle's Law:
According to Boyle's law, at constant temperature, the product of pressure and volume of a gas is constant. Mathematically, it can be expressed as:

P₁V₁ = P₂V₂

Where P₁ and V₁ represent the initial pressure and volume, and P₂ and V₂ represent the final pressure and volume respectively.

Definition of Isothermal Elasticity:
The isothermal elasticity of a gas, denoted by γ (gamma), is defined as the ratio of the relative change in pressure (∆P/P) to the relative change in volume (∆V/V) at constant temperature. Mathematically, it can be expressed as:

γ = (∆P/P) / (∆V/V)

Relation with Pressure:
From the equation of isothermal elasticity, it is evident that the isothermal elasticity is directly related to the relative change in pressure. Therefore, the isothermal elasticity of a gas is directly proportional to the change in pressure.

Relation with Volume:
Similarly, the isothermal elasticity is inversely related to the relative change in volume. Therefore, the isothermal elasticity of a gas is inversely proportional to the change in volume.

Answer:
Based on the above explanations, we can conclude that the isothermal elasticity of a gas is related to both pressure and volume. However, it is primarily determined by the change in pressure rather than the change in volume. Therefore, the correct answer is c) pressure. The isothermal elasticity of a gas is directly related to the change in pressure and is independent of factors such as density, volume, or specific heat.