An ideal gas (with C_p / C_V = ) undergoes a process where its pressure and volume are related by p = aV^b . Determine the value of b such that the specific heat capacity during this process equals zero.

Step-by-step solution

The specific heat capacity of a gas is zero when no heat is exchanged with the surroundings during the process, which means dQ = 0 . This condition corresponds to an adiabatic process. The equation for an adiabatic process is pV^ = constant . The given process equation is p = aV^b , which can be rewritten as pV^ -b = a . Comparing this with the equation of an adiabatic process, we get -b = . Therefore, b = - .