Gas equation pV = nRT is obey by ideal gas in (adiabatic/isothermal/both)?

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Solution

Isothermal process taking place in a thermodynamics system at constant temperature and adiabatic process taking place in a thermodynamic system for which there is no exchange of heat between the system and its surroundings. In both the process, the temperature is same or constant and these two process obeys Boyle’s law at constant temperature.
Therefore ideal gas equation pV = nRT is obeyed by ideal gas in both isothermal and adiabatic process.

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\begin{matrix} C o l u m n - I (I d e a l G a s) & Column - II (Related equation) (A) Reversible isothermal process & (P) W = - 2.303 n R T l o g (V_{2} / V_{1}) (B) Reversible adiabatic process & (Q) W = n C_{v, m} (T_{2} - T_{1}) (C) Irreversible adiabatic process & (R) P V = n R T (D) Irreversible isothermal process & (S) W = - \int_{v_{i}}^{v_{f}} P_{e x t .} d V \end{matrix}

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