An ideal gas undergoes a polytropic thermodynamic process where its pressure and volume satisfy the relation pressure multiplied by volume raised to the power of one point five equals a constant. If the gas is compressed to half of its initial volume, what is the ratio of its final temperature to its initial temperature?

💡 Solution & Explanation

In a polytropic process defined by pressure times volume to the power of n equals a constant, the relation between temperature and volume is derived by combining the ideal gas law where temperature is proportional to pressure times volume. Substituting pressure as constant divided by volume to power n yields temperature proportional to volume raised to the one minus n power. With n equal to one point five and final volume being half of initial volume, the temperature ratio becomes the inverse volume ratio raised to the negative zero point five power, resulting in two to the power of zero point five. Incorrect options fail to correctly apply the adiabatic or polytropic exponent indices in conjunction with the ideal gas equation of state. Specific heat capacities for monatomic and diatomic gases determine standard polytropic indices in engineering thermodynamics.