We have derived formulations for the pressure derivatives of bulk modulus up to the third order and for higher order Grüneisen parameters using the generalized free volume theory, and the generalized Rydberg equation of state. The properties derived in the present study are directly related to the understanding of thermoelastic properties of solids. The third order Grüneisen parameter (lambda λ) in the limit of infinite pressure has been found to approach a positive finite value for lambda infinity (λ∞) equal to 1/3. This is a result shown to be independent of the value of K-prime infinity, i. e., the pressure derivative of the bulk modulus at infinite pressure. The results based on other equations of state have also been reported and discussed. We find a relationship between λ∞ and pressure derivatives of bulk modulus at infinite pressure which is satisfied by different types of equations of state.

Thermodynamics of solids in the limit of infinite pressure formulated by Stacey reveals that the thermal expansivity (alpha) of solids tends to zero at infinite pressure. The earlier models for the volume dependence of thermal expansivity do not satisfy the infinite pressure behaviour of thermal expansivity. The expressions for the volume dependence of the isothermal Anderson-Grüneisen parameter (delta T) considered in the derivation of earlier formulations for alpha (V) have been found to be inadequate. A formulation for the volume dependence of delta T is presented here which is similar to the model due to Burakovsky and Preston for the volume dependence of the Grüneisen parameter. The new formulation for alpha (V) reveals that delta T infinity must be greater than zero for satisfying the thermodynamic result according to which alpha tends to zero at infinite pressure. It is found that our model fits well the experimental data on thermal expansivity alpha (V) for hcp iron corresponding to a wide range of pressures (0-360 GPa).

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The Anti-Lock Braking System (ABS) is one of the automotive industry safety functions. The vehicle's braking difficulty is lessened while its strength is boosted thanks to the installation of this safety system. Anti-Lock Hydraulic Brake tyre efficiency is improved as well since the roadway and the tyre are not eroded. However, this strategy does not work effectively in areas with bad road conditions. The latest advance known as the electronic brake power distribution to overcome the inconvenient automobile industry. "Electronic brake power distribution" is productive irrespective of whether street conditions such as frosty, watery, etc. are unfavourable. It also reduces braking and improves vehicle stability by incorporating utility in a control unit. The ABS is used in vehicles to prevent wheel bolting and slip after braking. The slip percentage shows the speed and rotation of the vehicle. Mechanized systems that suddenly require restrictions, rhythm braking that was boiling by convenient drivers with an earlier brake system are the subject of this investigation When the driver can respond more quickly, it's easier to steer. Driving assistance and distance limit spotting are provided by the ABS, alternatively on free surfaces such as gravel or snow secured asphalt, on illusive and dry surfaces. The anti-lock braking system may completely enhance braking distance even if vehicle control system is still improved.