Heat and Thermodynamics 4 Question 12

14. 2kg of a monoatomic gas is a pressure of 4×104N/m2. The density of the gas is 8kg/m3. What is the order of energy of the gas due to its thermal motion? (2019 Main, 10 Jan II)

(a) 106J

(b) 103J

(c) 104J

(d) 105J

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Solution:

  1. Given, mass of gas, m=2kg

Pressure on gas, p=4×104N/m2

Density of gas, ρ=8kg/m3

Volume of gas = Mass  Density 

V=28=14m3

Using ideal gas equation,

pV=nRTnRT=4×104×14nRT=104

Internal energy of n moles of a monoatomic gas is given by,

U=32nRTU=32×104J=1.5×104J

i.e. in order of 104J.



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