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Question
A sample of air weighing 1.18 g occupies 1.0 × 103 cm3 when kept at 300 K and 1.0 × 105 Pa. When 2.0 cal of heat is added to it at constant volume, its temperature increases by 1°C. Calculate the amount of heat needed to increase the temperature of air by 1°C at constant pressure if the mechanical equivalent of heat is 4.2 × 107 erg cal−1. Assume that air behaves as an ideal gas.
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Solution
Here,
m = 1.18 g = 1.18×10-3 kg
ΔQ = 2.0×4.2 J
P = 1.0×106 Pa
V = 1.0×103 cm3 = 1.0×10-3 m3
T = 300K
Applying eqn. of state
PV = nRT
=> n = PV/RT
=> n = 1.0×105×1.0×10-3/(8.314×300)
=> n = 0.04
ΔT = 10C
(ΔH)v = nCv ΔT
2.0×4.2 = nCv×1
=> Cv = 8.4/n= 8.4/0.04
=> Cv = 210
Again we know
Cp – Cv =R
=> Cp = R + Cv
=> Cp = 8.3 + 210
=> Cp = 218.3
Now at constant pressure
(ΔH)p = nCp ΔT
=> (ΔH)p = 218.3×0.04×1 = 8.732 J
In calories
=> (ΔH)p = 8.732/4.2 = 2.08 cal
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