The volumes of containers A and B, connected by a tube and a closed valve are V and 4 V, respectively. Both the containers A and B have the same ideal gas at pressures (temperatures) 5.0 andtimes;105Pa(300 K) and 1.0 andtimes;105Pa (400 K), respectively. The valve is opened to allow the pressure to equalise, but the temperature of each container is kept constant at its initial value. Find the common pressure in the containers.a)2.5 andtimes; 105Pab)2.0 andtimes; 105Pac)3.0 andtimes; 105Pad)1.5 andtimes; 105PaCorrect answer is option 'B'. Can you explain this answer?

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The volumes of containers A and B, connected by a tube and a closed valve are V and 4 V, respectively. Both the containers A and B have the same ideal gas at pressures (temperatures) 5.0 ×10⁵ Pa(300 K) and 1.0 ×10⁵Pa (400 K), respectively. The valve is opened to allow the pressure to equalise, but the temperature of each container is kept constant at its initial value. Find the common pressure in the containers.

a)
2.5 × 10⁵Pa
b)
2.0 × 10⁵Pa
c)
3.0 × 10⁵ Pa
d)
1.5 × 10⁵Pa

Correct answer is option 'B'. Can you explain this answer?

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The volumes of containers A and B, connected by a tube and a closed va...

∴ p₁ > p₂ so, the equalise pressure of the p is reduced from p₁

Given, T₁ = 300

T₂ = 400

V₂ = 4V

p₁ = 5 x 10⁵

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The volumes of containers A and B, connected by a tube and a closed va...

∴ p1 > p2 so, the equalise pressure of the p is reduced from p1

Given, T1 = 300

T2 = 400

V2 = 4V

p1 = 5 x 105

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The volumes of containers A and B, connected by a tube and a closed va...

Given data:

- Volume of container A = V
- Volume of container B = 4V
- Initial pressure and temperature of container A = 5.0 × 10^5 Pa and 300 K
- Initial pressure and temperature of container B = 1.0 × 10^5 Pa and 400 K

Pressure equalisation:

- When the valve is opened, the gas will flow from the higher pressure container (A) to the lower pressure container (B) until the pressure is equalized.
- Since the temperature of both containers remains constant during this process, according to Gay-Lussac's law, the pressure and temperature are directly proportional.

Calculation:

- Let P be the common pressure in both containers after equalization.
- Using the ideal gas law, we can write for container A initially: P1V = nRT1
- And for container B initially: P2(4V) = nR(400)
- After equalization, the total moles of gas in both containers remain constant. So, nR(300) = nR(400)
- Therefore, P1V = P(4V)
- P1 = 4P
- Since P1 = 5.0 × 10^5 Pa, we have: 5.0 × 10^5 = 4P
- Solving for P gives P = 1.25 × 10^5 Pa = 2.0 × 10^5 Pa

Therefore, the common pressure in the containers after equalization is 2.0 × 10^5 Pa, which corresponds to option B.

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The volumes of containers A and B, connected by a tube and a closed valve are V and 4 V, respectively. Both the containers A and B have the same ideal gas at pressures (temperatures) 5.0 ×105Pa(300 K) and 1.0 ×105Pa (400 K), respectively. The valve is opened to allow the pressure to equalise, but the temperature of each container is kept constant at its initial value. Find the common pressure in the containers.a)2.5 × 105Pab)2.0 × 105Pac)3.0 × 105Pad)1.5 × 105PaCorrect answer is option 'B'. Can you explain this answer?

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