The equation of state of a real gas is given by \[ \left( P + \frac{a}{V^2} \right)(V - b) = RT, \] where \( P, V \) and \( T \) are pressure, volume and temperature respectively and \( R \) is the universal gas constant. The dimensions of \[ \frac{a}{b^2} \] is similar to that of :
- PV
- R
- RT
- P
The Correct Option is D
Solution and Explanation
In the given equation of state for a real gas:
\(\left( P + \frac{a}{V^2} \right) (V - b) = RT,\)
the term \( \frac{a}{V^2} \) must have the same dimensions as pressure \( P \) since it is being added to \( P \).
The dimensional formula of pressure \( P \) is:
\([P] = [F][A^{-1}] = [M][L^{-1}][T^{-2}],\)
where \( F \) is force and \( A \) is area. Therefore, the dimensions of \( \frac{a}{V^2} \) must also be the same as \( P \).
Since \( \frac{a}{V^2} \) has the same dimensions as pressure
The correct option is (D) : P
Top Questions on Ideal gas equation
- Pressure of ideal gas at constant volume is proportional to _______.
- KCET - 2023
- Physics
- Ideal gas equation
- An air bubble having volume 1 cm3 at depth 40 m inside water comes to the surface. What will be the volume of the bubble at the surface?
- JEE Main - 2023
- Physics
- Ideal gas equation
- The correct relation between $\gamma=\frac{ c _{ p }}{ c _{ v }}$ and temperature $T$ is :
- JEE Main - 2023
- Physics
- Ideal gas equation
- The temperature of an ideal gas is increased from 200 K to 800 K. If r.m.s. speed of gas at 200K is v0. Then, r.m.s. speed of the gas at 800 K will be
- JEE Main - 2023
- Physics
- Ideal gas equation
- In the equation \(\bigg[X + {\frac{a}{Y^2}}\bigg] [Y - b] = RT\), X is pressure, Y is volume, R is universal gas constant and T is temperature. The physical quantity equivalent to the ratio \(\frac{a}{b}\) is
- JEE Main - 2023
- Physics
- Ideal gas equation
Questions Asked in JEE Main exam
- Let \[ \vec{a} = 2\hat{i} + \alpha \hat{j} + \hat{k}, \quad \vec{b} = -\hat{i} + \hat{k}, \quad \vec{c} = \beta \hat{j} - \hat{k}, \] where \( \alpha \) and \( \beta \) are integers and \( \alpha \beta = -6 \). Let the values of the ordered pair \( (\alpha, \beta) \) for which the area of the parallelogram of diagonals \( \vec{a} + \vec{b} \) and \( \vec{b} + \vec{c} \) is \( \frac{\sqrt{21}}{2} \), be \( (\alpha_1, \beta_1) \) and \( (\alpha_2, \beta_2) \). Then \( \alpha_1^2 + \beta_1^2 - \alpha_2 \beta_2 \) is equal to:
- JEE Main - 2024
- Vectors
- The molecular formula of second homologue in the homologous series of monocarboxylic acid is
- JEE Main - 2024
- Aldehydes, Ketones and Carboxylic Acids
- Given below are two statements: Statement I: $\text{PF}_5$ and $\text{BrF}_5$ both exhibit $\text{sp}^3\text{d}$ hybridisation.Statement II: Both $\text{SF}_6$ and $[\text{Co}(\text{NH}_3)_6]^{3+}$ exhibit $\text{sp}^3\text{d}^2$ hybridisation. In the light of the above statements,choose the correct answer from the options given below:
- JEE Main - 2024
- Hybridisation
- Consider the system of linear equations \( x + y + z = 4\mu \), \( x + 2y + 2\lambda z = 10\mu \), \( x + 3y + 4\lambda^2 z = \mu^2 + 15 \), where \( \lambda, \mu \in \mathbb{R} \). Which one of the following statements is NOT correct?
- JEE Main - 2024
- Linear Algebra
- If the constant term in the expansion of \((1 + 2x - 3x^3) \left(\frac{3}{2}x^2 - \frac{1}{3x}\right)^9\) is \( p \), then \( 108p \) is equal to _________.
- JEE Main - 2024
- Algebra
Concepts Used:
Ideal Gas Equation
An ideal gas is a theoretical gas composed of a set of randomly-moving point particles that interact only through elastic collisions.
What is Ideal Gas Law?
The ideal gas law states that the product of the pressure and the volume of one gram molecule of an ideal gas is equal to the product of the absolute temperature of the gas and the universal gas constant.
PV=nRT
where,
P is the pressure
V is the volume
n is the amount of substance
R is the ideal gas constant
Ideal Gas Law Units
When we use the gas constant R = 8.31 J/K.mol, then we have to plug in the pressure P in the units of pascals Pa, volume in the units of m3 and the temperature T in the units of kelvin K.