A rigid nitrogen tank stored inside a laboratory has a pressure of 30 atm at 06:00 am when the temperature is $27^{\circ} \mathrm{C}$. At 03:00 pm, when the temperature is $45^{\circ} \mathrm{C}$, the pressure in the tank will be $\_\_\_\_$ atm. [nearest integer]

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · States of Matter

A rigid nitrogen tank stored inside a laboratory has a pressure of 30 atm at 06:00 am when the temperature is

2 7^{\circ} C

. At 03:00 pm, when the temperature is

4 5^{\circ} C

, the pressure in the tank will be

____

atm. [nearest integer]

Answer: 32

Solution

For a rigid container (constant volume) with a fixed amount of gas, we use Gay-Lussac's Law:

\frac{P _{1}}{T _{1}} = \frac{P _{2}}{T _{2}}

Given:

P_{1} = 30

atm,

T_{1} = 27° C = 300

T_{2} = 45° C = 318

P_{2} = P_{1} \times \frac{T _{2}}{T _{1}} = 30 \times \frac{318}{300} = 30 \times 1.06 = 31.8 \approx 32 atm

Answer: 32

JEE Main · 2022 · 25 Jun 2022 · Shift 2 · Integer answer

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