Question

Choose the correct statement for the work done in the expansion and heat absorbed or released when 5 litres of an ideal gas at 10 atmospheric pressure isothermally expands into vacuum until volume is 15 litres :

• A. Both the heat and work done will be greater than zero
• B. Heat absorbed will be less than zero and work done will be positive
• C. Work done will be zero and heat will also be zero
• D. Work done will be greater than zero and heat will remain zero

Answer 1

Answer: (C)

Work done will be zero and heat will also be zero

Answer 2

This is a free expansion into a vacuum. In a free expansion, no work is done by the gas because the external pressure is zero.
Since the expansion is isothermal (constant temperature), the internal energy of the ideal gas remains constant $(\Delta U=0)$.
From the first law of thermodynamics, $\Delta U = q + w$, where q is heat absorbed and w is work done.
Since $\Delta U=0$ and $w=0$, the heat absorbed (q) is also zero.