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# 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.$\Delta {\text{E}} = \Delta {\text{H}} - {\text{P}}\Delta {\text{V}}$

Last updated date: 18th Jun 2024
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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.

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.