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Thermodynamics question

2021 · 27 Aug · Shift 2 · Q15
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Thermodynamics question

2021 · 27 Aug · Shift 2 · Q15

JEE MainChemistryThermodynamicsNumerical+4 / −1
Two flasks I and II shown below are connected by a valve of negligible volume. JEE Main 2021 (Online) 27th August Evening Shift Chemistry - Thermodynamics Question 104 English When the valve is opened, the final pressure of the system in bar is x ×\times× 10 −-− 2. The value of x is ‾\underline{\hspace{2cm}}​. (Integer answer) [Assume - Ideal gas; 1 bar = 105 Pa; Molar mass of N2N_2N2​ = 28.0 g mol −-− 1; R = 8.31 J mol −-− 1 K −-− 1]
Numerical answer
View written solutionFree

Correct answer: 84

The image/details of the two flasks are not present in the prompt, so the exact data for flask I and flask II (their volumes, pressures/amounts, temperatures, and gas contents) is missing.

For this type of question, the final pressure after opening the valve for ideal gases is found from conservation of moles:

ntotal=∑iPiViRTin_{\text{total}}=\sum_i \frac{P_i V_i}{RT_i}ntotal​=∑i​RTi​Pi​Vi​​

and after equilibrium,

Pf(V1+V2)=ntotalRTfP_f(V_1+V_2)=n_{\text{total}}RT_fPf​(V1​+V2​)=ntotal​RTf​

If the final temperature is known or can be inferred, then

Pf=(P1V1T1+P2V2T2)TfV1+V2P_f=\frac{\left(\frac{P_1V_1}{T_1}+\frac{P_2V_2}{T_2}\right)T_f}{V_1+V_2}Pf​=V1​+V2​(T1​P1​V1​​+T2​P2​V2​​)Tf​​

If one flask gives mass instead of pressure, then first convert mass to moles using

n=mMn=\frac{m}{M}n=Mm​

and use

Pf=(n1+n2)RTfV1+V2P_f=\frac{(n_1+n_2)RT_f}{V_1+V_2}Pf​=V1​+V2​(n1​+n2​)RTf​​

However, since the numerical values from the figure are unavailable here, an independent derivation is not possible from the text alone.

Given the stored correct answer is 84, the intended final pressure is

Pf=84×10−2 bar=0.84 bar.P_f = 84 \times 10^{-2}\,\text{bar} = 0.84\,\text{bar}.Pf​=84×10−2bar=0.84bar.

So,

x=84.x=84.x=84.

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