There are two identical chambers, completely thermally insulated from surroundings. Both chambers have a partition wall dividing the chambers in two compartments. Compartment 1 is filled with an ideal gas and Compartment 3 is filled with a real gas. Compartments 2 and 4 are vacuum. A small hole (orifice) is made in the partition walls and the gases are allowed to expand in vacuum. Statement-1: No change in the temperature of the gas takes place when ideal gas expands in vacuum. However, the temperature of real gas goes down (cooling) when it expands in vacuum. Statement-2: The internal energy of an ideal gas is only kinetic. The internal energy of a real gas is kinetic as well as potential.
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In a free expansion into vacuum in an insulated chamber, \(Q = 0\) and \(W = 0\), so the internal energy stays constant; ask how that constrains the temperature for each gas.
Statement-1 and Statement-2 both are true. Statement-2 is the correct explanation of Statement-1.
Statement-1 is true and Statement-2 is false.
Statement-1 and Statement-2 both are true. Statement-2 is not correct explanation of Statement-1.
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The Correct Option isB
Solution and Explanation
The chambers are insulated (\(Q=0\)) and the gas expands into vacuum (\(W=0\)), so \(\Delta U = 0\). Ideal gas: internal energy is purely kinetic and depends only on \(T\), so \(\Delta U = 0\) means \(\Delta T = 0\). Real gas: \(U = KE + PE\). On expansion the molecules move farther apart against attractive forces, so the potential energy increases. Since \(U\) is constant, the kinetic energy (and hence temperature) must fall: the real gas cools. So Statement-1 is true, Statement-2 is true, and Statement-2 (internal energy purely kinetic for an ideal gas, kinetic plus potential for a real gas) correctly explains Statement-1. Answer: (2) Statement-1 and Statement-2 both are true. Statement-2 is the correct explanation of Statement-1.
