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Thermodynamic State Variables And Equation Of State - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Syllabus

Quick Facts

Thermodynamic variables and equation of state is considered one of the most asked concept.
5 Questions around this concept.

Solve by difficulty

MEDIUM

One mole of an ideal gas passes through a process where pressure and volume obey the

relation $P = P_0 [ 1- \frac{1}{2}\left ( \frac{V_0}{V} \right )^2]$ .Here $P_0$ and $V_0$ are constant . Calculate the change in temperature of gas if its volume changes from $V_0 \: \: to \: \: 2 V_0$

$\frac{1P_0 V_0 }{2R}$

$\frac{5 P_0 V_0 }{4 R}$

$\frac{3 P_0 V_0 }{4 R}$

$\frac{ P_{0} V_{0}}{4 R}$

View Solution

$\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^2}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$ represents the equation of state of some gases. Where P is the pressure, V is the volume, T is the temperature and a, b, R are the constants. The physical quantity, which has dimensional formula as that of $\frac{b^{2}}{a}$ will be:

Compressibility

Energy density

Modulus of rigidity

Bulk modulus

View Solution

Concepts Covered - 1

Thermodynamic variables and equation of state

Thermodynamic variables : Any thermodynamic system can be described by specifying some of the variables i.e; its pressure(P), volume(V), temperature(T), internal energy(U) and the number of moles(n). These parameters are called thermodynamic variables.

Extensive and Intensive properties/variables -

Intensive properties do not depend on the amount of matter that is present. These are bulk properties. Examples of intensive properties are - Density, Temperature ets.
Extensive properties are those properties which depend on the amount of matter that is present. Examples of extensive properties are - Volume, Weight etc.

Equation of state - The relation between the thermodynamic variables (P, V, T) of the system is called equation of state.

For n moles of an ideal gas, equation of state is PV = nRT

For n moles of a real gas equation of state is $(P + \frac{an^{2}}{V^{2}})(V- nb) = nRT$

Thermodynamic process : The process of change of state of a system involves change of thermodynamic variables such as pressure P, volume V and temperature T of the system. The process is known as thermodynamic process.

Some important processes are -

(i) Isothermal process (ii) Adiabatic process (iii) Isobaric process (iv) Isochoric process

(v) Cyclic and non-cyclic process (vi) Reversible and irreversible process

Later, we will study all these process one by one in detail.

State and path function -

State or Point function does not depend on the path followed by the thermodynamic process but it depends on the final and initial position of the process.

Path function depends on the path followed by a thermodynamic process and not on the initial and final states of the system. Example of point function is Internal energy and example of path function is Heat and work.