6. (JEE Main 2022 (Online) 29th June Morning Shift )

In van der Waal equation $[P + \frac{a}{V^{2}}]$ [V $-$ b] = RT; P is pressure, V is volume, R is universal gas constant and T is temperature. The ratio of constants $\frac{a}{b}$ is dimensionally equal to :

(A) $\frac{P}{V}$

(B) $\frac{V}{P}$

(C) PV

(D) PV³

Correct answer is (C)

From the equation

$[a] \equiv [P V^{2}]$

$[b] \equiv [V]$

$\Rightarrow [\frac{a}{b}] \equiv [P V]$

7. (JEE Main 2022 (Online) 27th June Evening Shift )

For a perfect gas, two pressures P₁ and P₂ are shown in figure. The graph shows :

JEE Main 2022 (Online) 27th June Evening Shift Physics - Heat and Thermodynamics Question 101 English

(A) P₁ > P₂

(B) P₁ < P₂

(C) P₁ = P₂

(D) Insufficient data to draw any conclusion

Correct answer is (A)

As per ideal gas equation, $V = \frac{n R}{P} T$

$\Rightarrow$ Slope of V-T graph is inversely proportional to P.

As m₂ > m₁ $\Rightarrow$ P₁ > P₂

8. (JEE Main 2022 (Online) 27th June Morning Shift )

A mixture of hydrogen and oxygen has volume 2000 cm³, temperature 300 K, pressure 100 kPa and mass 0.76 g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be:

[Take gas constant R = 8.3 JK^{$-$ 1}mol^{$-$ 1}]

(A) $\frac{1}{3}$

(B) $\frac{3}{1}$

(C) $\frac{1}{16}$

(D) $\frac{16}{1}$

Correct answer is (B)

$P_{1} V = n_{1} R T$

$P_{2} V = n_{2} R T$

$\Rightarrow$ (100 kPa) V = (n₁ + n₂)RT

$\Rightarrow n_{1} + n_{2} = \frac{(100 k P a) (2000 c m^{3})}{8.3 \times 300}$ ..... (1)

Also, n₁ $\times$ 2 + n₂ $\times$ 32 = 0.76 ...... (2)

Solving (1) and (2),

n₁ = 0.06

n₂ = 0.02

$\Rightarrow \frac{n_{1}}{n_{2}} = 3$

9. (JEE Main 2022 (Online) 25th June Evening Shift )

When a gas filled in a closed vessel is heated by raising the temperature by 1 $^{\circ}$ C, its pressure increases by 0.4%. The initial temperature of the gas is ___________ K.

Correct answer is (250)

$P V = n R T$

So $\frac{d P}{P} \times 100 = \frac{d T}{T} \times 100$

$0.4 = \frac{1}{T} \times 100$

$\Rightarrow T = 250 K$

10. (JEE Main 2021 (Online) 31st August Evening Shift )

A mixture of hydrogen and oxygen has volume 500 cm³, temperature 300 K, pressure 400 kPa and mass 0.76 g. The ratio of masses of oxygen to hydrogen will be :-

(A) 3 : 8

(B) 3 : 16

(C) 16 : 3

(D) 8 : 3

Correct answer is (C)

PV = nRT

400 $\times$ 10³ $\times$ 500 $\times$ 10^{$-$ 6} = n $(\frac{25}{3})$ (300)

n = $\frac{2}{25}$

n = n₁ + n₂

$\frac{2}{25}$ = $\frac{M_{1}}{2} + \frac{M_{2}}{32}$

Also, M₁ + M₂ = 0.76 gm

$\frac{M_{2}}{M_{1}} = \frac{16}{3}$

Kinetic Theory of Gases