An ideal gas expands from volume $V_1$ to $V_2$. This may be achieved by either of the three processes: isobaric, isothermal and adiabatic. Let $\Delta U$ be the change in internal energy of the gas, $Q$ be the quantity of heat added to the system and $W$ be the work done by the system on the gas. Identify which of the following statements is false for $\Delta U$?
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We know that, $\Delta U \propto \Delta T$
For isotherm, $\Delta T=0 \Rightarrow \Delta U=0$
For adiabat, $\Delta Q=0 \Rightarrow \Delta U=-\Delta W<0$
For isobar, $\Delta V \propto \Delta T \Rightarrow \Delta T>0 \Rightarrow \Delta U>0$
Let the internal energy change be $\Delta U_{1}, \Delta U_{2}, \Delta U_{3}$ for the isotherm, adiabat, isobar respectively.
Then $\Delta U_{3}>\Delta U_{1}>\Delta U_{2}$
Thus option $b$ is only false
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