In a closed insulated container a liquid is stirred with a paddle to increase the temperature, which of the…
In a closed insulated container a liquid is stirred with a paddle to increase the temperature, which of the following is true?
$\Delta \mathrm{U}=w \neq 0, q=0$
$\Delta \mathrm{U}=w=q \neq 0$
$\Delta \mathrm{U}=0, w=q \neq 0$
$w=0, \Delta \mathrm{U}=q \neq 0$
Solution
System is in a closed container. So there will be no heat transfer. Therefore the heat is $q=0$. Now liquid is stirred with a paddle to increase the temperature which increases the internal energy $\Delta E$ of the system.
$\begin{aligned}
& \Delta \mathrm{E}=n \mathrm{C} \Delta \mathrm{T} \\
& \Delta \mathrm{E} \neq 0
\end{aligned}$
Work is also done on the system when started with a paddle.
$\begin{gathered}
\mathrm{W} \neq 0 \\
\Delta \mathrm{E}=q+\mathrm{W}=0+\mathrm{W}, \Delta \mathrm{E}=\mathrm{W} \\
\Delta \mathrm{E}=\Delta \mathrm{W} \neq 0, q=0
\end{gathered}$