2 moles of an ideal gas undergo isothermal expansion at 300 K into a vacuum, such that its volume changes from 2 L to 10 L . What are the values of the change in internal energy ( U ) and the change in enthalpy ( H ) for this process?

Step-by-step solution

For an ideal gas, the internal energy depends only on temperature. Since the process is isothermal, the change in temperature is zero ( T = 0 ). Therefore, the change in internal energy is zero ( U = nC_v T = 0 J ). The change in enthalpy is given by the relation H = U + (PV) . For an ideal gas, PV = nRT . Since the temperature is constant, PV is constant, which means (PV) = 0 . Substituting these values yields H = 0 + 0 = 0 J . Alternatively, for an ideal gas, enthalpy also depends only on temperature ( H = nC_p T