inexact differential meaning in Hindi

Examples

1. Thus, infinitesimal increments of heat and work are inexact differentials.
2. The lowercase Greek letter delta,, is the symbol for inexact differentials.
3. The quantity dY is an exact differential, while \ delta X is not, it is an inexact differential.
4. This is because there can be no unique representation of an antiderivative for inexact differentials since their variation is inconsistent along different paths.
5. For this reason, the increment \ delta Q \ is said to be an'imperfect differential'or an'inexact differential '.
6. The symbol " ? " will be reserved for an inexact differential, which cannot be integrated without full knowledge of the path.
7. The integral of any inexact differential over the time it takes for a system to leave and return to the same thermodynamic state does not necessarily equal zero.
8. Following the definition above in formula ( 1 ), for such a fictive'reversible'process, a quantity of transferred heat ( an inexact differential ) is analyzed as a quantity, with ( an exact differential ):
9. The ?'s before the heat and work terms are used to indicate that they describe an increment of energy which is to be interpreted somewhat differently than the \ mathrm { d } U increment of internal energy ( see Inexact differential ).
10. It is commonly used to solve ordinary differential equations, but is also used within multivariable calculus when multiplying through by an integrating factor allows an inexact differential to be made into an exact differential ( which can then be integrated to give a scalar field ).