Question

An ideal gas expands from volume $V_1$ to $V_2$. This may be achieved by either of 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 $\Delta U$?

• A. $\Delta U$ is least under adiabatic process
• B. $\Delta U$ is greatest under adiabatic process
• C. $\Delta U$ is greatest under isobaric process
• D. $\Delta U$ is isothermal process lies between the values obtained under isobaric and adiabatic processes

Answer 1

Answer: (B)

$\Delta U$ is greatest under adiabatic process

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