An ideal gas is expanded from \( \left(\mathrm{p}_{1}, \mathrm{~V}_{1}, \mathrm{~T}_{1}\right) \....

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An ideal gas is expanded from \( \left(\mathrm{p}_{1}, \mathrm{~V}_{1}, \mathrm{~T}_{1}\right) \) to \( \left(\mathrm{p}_{2}\right. \), \( \mathrm{V}_{2}, \mathrm{~T}_{2} \) ) under different conditions. The correct statements(s) among the following is(are)
(1) The work done by the gas is less when it is expanded reversibly from \( V_{1} \) to \( V_{2} \) under adiabatic conditions as compared to that when expanded reversibly from \( V_{1} \) to \( V_{2} \) under isothermal conditions.
(2) The change in internal energy of the gas is (i) zero, if it is expanded reversibly with \( \mathrm{T}_{1}=\mathrm{T}_{2} \), and (ii) positive, if it is expanded reversibly under adiabatic conditions with \( \mathrm{T}_{1} \neq \mathrm{T}_{2} \).
(3) If the expansion is carried out freely, it is simultaneously both isothermal as well as adiabatic
(4) The work done on the gas is maximum when it is compressed irreversibly from \( \left(\mathrm{p}_{2}, \mathrm{~V}_{2}\right) \) to \( \left(\mathrm{p}_{1}, \mathrm{~V}_{1}\right) \) against constant pressure \( \mathrm{p}_{1} \)


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