Read the following statements regarding thermodynamic processes:...

Statement I is correct: From the First Law of Thermodynamics, $Q = \Delta U + W$. If $Q$ and $\Delta U$ are the same, the work done $W$ is the same. Work done at constant pressure is $W = P \Delta V = P(\pi r^2)x$. For $W$ and $P$ to be constant, $r^2 x$ must be constant. If $r$ is doubled, $r^2$ becomes four times, so $x$ must become one-fourth.

Statement II is correct: In an isothermal process for an ideal gas, the change in internal energy $\Delta U = 0$. Therefore, $Q = W$, meaning all supplied heat is converted into work.

Statement III is incorrect: At constant pressure, $W = nR\Delta T$ and $Q = nC_p\Delta T$. The ratio $\dfrac{W}{Q} = \dfrac{R}{C_p}$. Since molar heat capacity at constant pressure ($C_p$) depends on the atomicity of the gas, the work done for a given amount of heat will vary for gases with different atomicity.

Statement IV is incorrect: Work done $W = P(\pi r^2)x$. For a given displacement $x$ and constant pressure $P$, the work done is directly proportional to the square of the radius ($r^2$), not the radius ($r$).

Therefore, exactly two statements (I and II) are correct.

Answer: Two