Question

Under Which of the following condition is the relation,
$\Delta H = \Delta U + P\Delta V$ valid for a closed system?
A. Constant pressure
B. Constant temperature
C. Constant temperature and pressure
D. Constant temperature, pressure and composition

Answer 1

Hint: The equation \[\Delta H = \Delta U + P.\Delta V\]comes from the first law of thermodynamics.
At constant temperature internal energy of the system remains constant.

Complete step by step answer:
Internal energy of a system is basically the sum of kinetic energy and potential energy of the particles present in that system. In case of ideal gas as the particles do not interact with each other, so the total internal energy is due the kinetic energy of the system.
Enthalpy is the transfer of energy in a chemical reaction or a system. Enthalpy of a system is the sum of internal energy of the system plus the product of pressure and volume of the system.
\[H = U + PV\]
If we calculate the change in enthalpy of the system, then
\[\Delta H = \Delta U + \Delta (PV)\]
\[\Delta H = \Delta U + \Delta P.V + P.\Delta V\]
At constant temperature,$\Delta T = 0$ this implies that the change in internal energy is also equal to $0$ or, $\Delta U = 0$. So, the above equation will become \[\Delta H = \Delta P.V + P.\Delta V\].
At constant pressure, \[\Delta P = 0\]. So, the equation will be \[\Delta H = \Delta U + P.\Delta V\].
Basically, the equation \[\Delta H = \Delta U + P.\Delta V\]comes from the first law of thermodynamics. The first law of thermodynamics states that change in heat energy of the system is equal to the sum of change in internal energy of the system and work done by the system. At constant pressure, change in enthalpy is equal to the change in heat energy of the system and \[P.\Delta V\] is the work done by the system.
At constant temperature and pressure, both $\Delta T = 0$ and \[\Delta P = 0\]. Which implies that \[\Delta H = P.\Delta V\].
So, the equation \[\Delta H = \Delta U + P.\Delta V\]is valid at constant pressure only for a closed system.

Hence, the correct answer is \[\left( A \right)\].

Note:
If a system is maintained at constant temperature it is called isothermal, at constant pressure it is called isobaric, at constant volume it is called isochoric and at constant heat it is called adiabatic.