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A Sample of Air Weighing 1.18 G Occupies 1.0 × 103 Cm3 When Kept at 300 K and 1.0 × 105 Pa. - Physics

Answer in Brief

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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APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 5 Specific Heat Capacities of Gases
Q 6 | Page 77
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