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Question
An ideal gas expands from 100 cm3 to 200 cm3 at a constant pressure of 2.0 × 105 Pa when 50 J of heat is supplied to it. Calculate (a) the change in internal energy of the gas (b) the number of moles in the gas if the initial temperature is 300 K (c) the molar heat capacity Cp at constant pressure and (d) the molar heat capacity Cv at constant volume.
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Solution
Initial volume of the gas, V1 = 100 cm3
Final volume = V2 = 200 cm3
Pressure = 2 × 105 Pa
Heat supplied, dQ = 50 J
(a) According to the first law of thermodynamics,
dQ = dU + dW
dW = PΔV = 2 × 105 × (200 -100) × 10-6 = 20
Initial volume of the gas, V1 = 100 cm3
Final volume = V2 = 200 cm3
Pressure = 2 × 105 Pa
Heat supplied, dQ = 50 J
(a) According to the first law of thermodynamics,
dQ = dU + dW
`"U" = 3/2 "n""R""T"`
`30 = n xx 3/2 xx 8.3 xx 300`
`=> n = 2/(83 xx3) = 2/249 = 0.008`(c) Also,
dU = nCvdT
`=> "C"_"V" = ("d""U")/ ("n""d""T") = 30 /(0.008 xx 300) = 12.5`
Cp = Cv + R = 12.5 + 8.3 = 20.8 J/mol-K
(d) Cv = 12.5 J/mol-K
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