Correct Answer - Option 1 :
\(\frac{P}{T} = C\) ;
\(\frac{V}{T} = C\)
The correct answer is option 1) i.e. \(\frac{P}{T} = C\) ; \(\frac{V}{T} = C\)
CONCEPT:
The equation for the thermodynamic state of a gas is given by:
PV = nRT
Where P is the pressure, V is the volume, T is the temperature, n is the number of moles of the gas and R is the universal gas constant (8.314 J mol-1 K-1)
-
Isochoric process: It is a thermodynamic process where the volume of the system undergoes no change i.e. remains constant.
-
Isobaric process: It is a thermodynamic process where the pressure of the system undergoes no change i.e. remains constant.
EXPLANATION:
In a given thermodynamic system, the number of moles (n) and universal gas constant (R) remains constant in the equation of thermodynamic state.
Therefore, PV = CT
Where C represents a constant value.
For an isochoric process, volume V is constant. ⇒ PV = nRT ⇒\(\frac{P}{T} = \frac{C}{V} = C\)
For an isobaric process, pressure P is constant. ⇒ PV = nRT ⇒\(\frac{V}{T} = \frac{C}{P} = C\)
