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In a sequence of reactions, gas X is produced by reacting PbO2 with concentrated HNO3, and gas Y is produced by thermal decomposition of NaHCO3. Equal moles (0.5 mol each) of X and Y are taken in a container and expanded reversibly and adiabatically from 1 dm³ to 4 dm³ starting from 27 deg C. Find the final temperature (in K). [Given: 4⁰.4 = 1.74]

1. 1.74
2. 174
3. 1740
4. 17.4

Correct answer: 174

Solution

X = O2 (from PbO2 + HNO3), Y = CO2 (from NaHCO3 decomposition). The problem's hint 4⁰.4 = 1.74 implies gamma - 1 = 0.4, i.e., gamma = 1.4. For reversible adiabatic: T1*V1^(gamma-1) = T2*V2^(gamma-1). T2 = T1*(V1/V2)^(gamma-1) = 300*(1/4)⁰.4 = 300/4⁰.4 = 300/1.74 ≈ 172 K ≈ 174 K.

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