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An ideal gas in a cylinder is compressed adiabatically to one-third of its original volume. A work of $45 \mathrm{~J}$ is done on the gas by the process. The change in internal energy of the gas and the heat flowed into the gas, respectively are
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The correct answer is:
$45 \mathrm{~J}$ and zero
For adiabatic process, $\Delta Q=0$
Now, from first law of thermodynamics, we have
$$
\Delta Q=\Delta U+\Delta W
$$
$\Delta W=-45$ or work is done on the gas.
$$
\begin{array}{lc}
\Rightarrow & 0=\Delta U-45 \\
\Rightarrow & \Delta U=45 \mathrm{~J}
\end{array}
$$
Now, from first law of thermodynamics, we have
$$
\Delta Q=\Delta U+\Delta W
$$
$\Delta W=-45$ or work is done on the gas.
$$
\begin{array}{lc}
\Rightarrow & 0=\Delta U-45 \\
\Rightarrow & \Delta U=45 \mathrm{~J}
\end{array}
$$
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