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in Kinetic Theory of Gases by (49.6k points)
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A vessel has 0.014 kg nitrogen gas filled at 27°C. How much heat would be provided to increase the root mean square speed by two times?

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Initial temperature of gas
T = 273 + 27 = 300 K
∵ Root mean square velocity, υrms ∝ \(\sqrt { T }\)
Hence, to double the r.m.s. velocity the temperature should be 4 times the intial velocity.
Hence, increase in temperature
= 4T – T = 3T = 3 × 300 = 900 K
Molecular weight of nitrogen is 28, hence mass of 1 mol is 28.
Hence in 0.014 kg or 14 g nitrogen, number of moles are;

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