During a reversible isothermal compression, 0.5 ~mol of an ideal gas at 400 ~K is compressed from a pressure of 2 ~atm to 10 ~atm . What is the change in internal energy ( U ) for the gas? (Given: R = 8.314 ~J ~K ⁻¹ ~mol ⁻¹ , 5 = 0.699 )

Step-by-step solution

For an ideal gas, the internal energy depends only on its temperature. In an isothermal process, the temperature of the system remains constant, which means T = 0 . The change in internal energy is given by the relation U = n C_v T . Since T = 0 , it follows that U = 0 ~J . Answer: 0 ~J