Question

Which is not the correct relation between enthalpy \[\left( {\Delta {\text{H}}} \right)\] and intrinsic energy \[\left( {\Delta {\text{E}}} \right)\]
A.\[\Delta {\text{H}} = \Delta {\text{E}} + {\text{P}}\Delta {\text{V}}\]
B.\[\Delta {\text{H}} = \Delta {\text{E}} + {\text{nRT}}\]
C.\[\Delta {\text{H}} = \Delta {\text{E}} - {\text{P}}\Delta {\text{V}}\]
D.\[\Delta {\text{E}} = \Delta {\text{H}} - {\text{P}}\Delta {\text{V}}\]

Answer 1

Hint: To answer this we must know the relation between enthalpy and intrinsic energy. Rearranging the formula will give us the above mentioned options; one of them is incorrectly represented. Take the help of the ideal gas equation.
Formula used: \[\Delta {\text{H}} = \Delta {\text{E}} + {\text{P}}\Delta {\text{V}}\]
Here Enthalpy is \[\left( {\Delta {\text{H}}} \right)\] and intrinsic energy or internal energy is \[\left( {\Delta {\text{E}}} \right)\] , P is pressure and V is volume.

Complete step by step answer:
The actual relationship between the enthalpy and the energy is as follow:
\[\Delta {\text{H}} = \Delta {\text{E}} + {\text{P}}\Delta {\text{V}}\]
So, the given relation in option A stands correct.
Now if we rearrange the formula by moving the factor \[{\text{P}}\Delta {\text{V}}\] to the enthalpy side. We need to put the negative sign before \[{\text{P}}\Delta {\text{V}}\] . The equation will become:
\[\Delta {\text{E}} = \Delta {\text{H}} - {\text{P}}\Delta {\text{V}}\]
This is the same as the option D. So option D is also correct.
We know the ideal gas equation. The ideal gas equation says that:
\[{\text{P}}\Delta {\text{V}} = {\text{nRT}}\]
We can substitute the value of \[{\text{P}}\Delta {\text{V}}\] in the main formula. We will get the following equation:
\[\Delta {\text{H}} = \Delta {\text{E}} + {\text{nRT}}\]
Hence, the given option B is correct.
There is no possible arrangement in which we can get the option C. Hence it is incorrect representation.

Thus, the correct option is C.

Note:
Enthalpy is defined as the sum of internal energy and product of pressure and volume. The heat absorbed or released in a system at constant pressure is known as enthalpy change. The energy present or stored within a substance is known as internal energy. Internal energy is a state function and is an extensive quantity. This means it depends upon the quantity of material and not on the nature. The negative of \[{\text{P}}\Delta {\text{V}}\] is known as work done in thermodynamics.