The following graph represents the T-V curves of an ideal gas ( where T is the temperature and V the volume) at three pressures P1, P2 and P3 compared with those of Charles's law represented as dotted lines.
Then the correct relation is :
The following graph represents the T-V curves of an ideal gas ( where T is the temperature and V the volume) at three pressures P1, P2 and P3 compared with those of Charles's law represented as dotted lines.
Then the correct relation is :
- P3 > P2 > P1
- P1 > P3 > P2
- P2 > P1 > P3
- P1 > P2 > P3
The Correct Option is D
Approach Solution - 1
Step 1: Recall Charles’s Law
Charles’s law states that at constant pressure, the volume of an ideal gas is directly proportional to its temperature:
$$ V \propto T \quad \text{(at constant P)} $$
Step 2: Analyze the Graph
In the Temperature-Volume (T-V) graph, the slope of each curve represents:
$$ \text{Slope} = \frac{1}{P} $$
Since pressure (P) is constant for a given curve, a steeper slope indicates a lower pressure.
Step 3: Compare the Slopes
\( P_1 \) has the least slope, indicating the highest pressure.
\( P_3 \) has the steepest slope, indicating the lowest pressure.
Step 4: Conclusion
The correct order of pressures is:
$$ P_1 > P_2 > P_3 $$
Approach Solution -2
Step 1: Recall Charles’s Law
Charles’s law states that at constant pressure, the volume of an ideal gas is directly proportional to its temperature:
$$ V \propto T \quad \text{(at constant P)} $$
Step 2: Analyze the Graph
In the Temperature-Volume (T-V) graph, the slope of each curve represents:
$$ \text{Slope} = \frac{1}{P} $$
Since pressure (P) is constant for a given curve, a steeper slope indicates a lower pressure.
Step 3: Compare the Slopes
- \( P_1 \) has the least slope, indicating the highest pressure.
- \( P_3 \) has the steepest slope, indicating the lowest pressure.
Step 4: Conclusion
The correct order of pressures is:
$$ P_1 > P_2 > P_3 $$
Top Questions on Ideal Gases
- A container has two chambers of volumes \(V_1 = 2\) litres and \(V_2 = 3\) litres separated by a partition made of a thermal insulator. The chambers contain \(n_1 = 2\) moles and \(n_2 = 3\) moles of ideal gas at pressures \(p_1 = 1\) atm and \(p_2 = 2\) atm, respectively. When the partition is removed, the mixture attains an equilibrium pressure of :
- NEET (UG) - 2025
- Physics
- Ideal Gases
- A vessel of volume \( V \) L contains an ideal gas at \( T(K) \). The vessel is partitioned into two equal parts. The volume (in L) and temperature (in K) in each part is respectively:
- AP EAMCET - 2024
- Chemistry
- Ideal Gases
- The canonical partition function of an ideal gas is given by \( Q(T,V,N) = \frac{1}{N!} \left( \frac{V}{\lambda(T)^3} \right)^N \), where \( T \), \( V \), \( N \), and \( \lambda(T) \) denote temperature, volume, number of particles, and thermal de Broglie wavelength, respectively. Let \( k_B \) be the Boltzmann constant and \( \mu \) be the chemical potential. Using \( \ln(N!) = N \ln(N) - N \), if the number density \( \left( \frac{N}{V} \right) \) is \( 2.5 \times 10^{25} \) m\(^{-3} \) at temperature \( T \), then \( e^{\mu/(k_B T)} / (\lambda(T))^3 \times 10^{-25} \) is ___ m\(^{-3} \) (rounded off to one decimal place).
- GATE PH - 2024
- Physics
- Ideal Gases
- When a bottle of soda water is opened, carbon dioxide escapes, producing a fizz. This is due to:
- What is the relation between Boyle temperature (TB) and critical temperature (Tc) of a gas?
- CUET (PG) - 2023
- Physics
- Ideal Gases
Questions Asked in NEET exam
Predict the major product $ P $ in the following sequence of reactions:
(i) HBr, benzoyl peroxide
(ii) KCN
(iii) Na(Hg), $C_{2}H_{5}OH$- NEET (UG) - 2025
- Organic Chemistry
- Which one of the following compounds can exist as cis-trans isomers?
- NEET (UG) - 2025
- Organic Chemistry
- Two identical charged conducting spheres A and B have their centres separated by a certain distance. Charge on each sphere is \(q\) and the force of repulsion between them is \(F\). A third identical uncharged conducting sphere C is brought in contact with sphere A first and then with sphere B and finally removed from both. New force of repulsion between spheres A and B (Radius of A and B are negligible compared to the distance of separation so that they can be considered as point charges) is best given as:
- NEET (UG) - 2025
- Coulomb’s Law
- An electron (mass \(9 \times 10^{-31}\) kg and charge \(1.6 \times 10^{-19}\) C) moving with speed \(c/100\) (\(c\) = speed of light) is injected into a magnetic field of magnitude \(9 \times 10^{-4}\) T perpendicular to its direction of motion. We wish to apply a uniform electric field \( \vec{E} \) together with the magnetic field so that the electron does not deflect from its path. (speed of light \(c = 3 \times 10^8\) m/s):
- NEET (UG) - 2025
- Electric Field
- Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): All vertebrates are chordates but all chordates are not vertebrates.
Reason (R): The members of subphylum Vertebrata possess a notochord during the embryonic period; the notochord is replaced by a cartilaginous or bony vertebral column in adults.