Answer-An ideal gas expands into vacuum in an insulated container. Then:

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The process described is the free expansion of an ideal gas into a vacuum in an insulated container.    Work Done W The gas expands into a vacuum. This means there is no external pressure opposing the expansion. The work done by the gas is given by WPext dV. Since the external pressure Pext is zero expansion into a vacuum, the work done by the gas is W0  dV0 So, W0.   Heat Exchange Q The container is insulated, which means there is no heat exchange between the system the gas and its surroundings. Therefore, the heat added to or removed from the system is zero Q0   Change in Internal Energy U According to the first law of thermodynamics, the change in internal energy of a system is given by UQW Substituting the values we found for Q and W U000 So, U0.   For an ideal gas, the internal energy depends only on its temperature. Since the internal energy remains constant U0, the temperature of the ideal gas also remains constant during free expansion.  Therefore, U0, Q0, and W0. This corresponds to option A.

An ideal gas expands into vacuum in an insulated container. Then:

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