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प्रश्न
Standing waves of frequency 5.0 kHz are produced in a tube filled with oxygen at 300 K. The separation between the consecutive nodes is 3.3 cm. Calculate the specific heat capacities Cp and Cv of the gas.
उत्तर
Frequency of standing waves, f = 5 × 103 Hz
Temperature of oxygen, T = 300 K
From Kundt's tube theory, we know that`"l" / 2` = node separation = 3.3 cm
∴ l = 6.6 × 10−2 m
Also,
v = fl = 5 × 103 × 6.6 × 10−2
= (66 × 5) = 330 m/s
`"v" = sqrt((gamma "R""T")/"M")`
`"v"^2=(gamma "R""T")/"M"`
`therefore gamma = (330 xx 330 xx 32)/(8.3 xx 300 xx 100 ) = 1.3995`
Specific heat at constant volume , `"C"_"v" = "R"/(gamma -1) = 8.3/0.3995`
= 20.7 J mol -K
Specific heat at constant pressure, Cp = Cv + R
Cp = 20.7 + 8.3
Cp = 29.0 J/mol-K
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