The isothermal bulk modulus of elasticity of a gas is 1.5 * 100000 N/m^2. What will be its adiabatic bulk modulus of elasticity? Given the ratio of Cp/Cv=1.4
isothermal bulk modulus of elasticity K(T) = P
adiabatic bulk modulus of elasticity K(a) = γP,
where P is the pressure,
γ = C(p)/ C(v) is ratio of specific heats – adiabatic exponent
K(a) =γ• K(T) = 1.4•1.5•10^5 =
=2.1•10^5 N/m^2
To find the adiabatic bulk modulus of elasticity of a gas, we can use the relationship between the isothermal bulk modulus (K) and the adiabatic bulk modulus (Kad) expressed in terms of the adiabatic index (γ), which is the ratio of specific heat capacities at constant pressure (Cp) to constant volume (Cv).
The relationship is given by:
Kad = K * (Cp/Cv)
Given that the isothermal bulk modulus (K) is 1.5 * 100000 N/m^2 and the ratio of specific heat capacities (Cp/Cv) is 1.4, we can substitute these values into the equation to find Kad:
Kad = (1.5 * 100000) * 1.4
Kad = 210000 N/m^2
Therefore, the adiabatic bulk modulus of elasticity of the gas is 210000 N/m^2.