Dare to pressurize a gas? #1
Classical Mechanics
Level
3
A Diatomic ideal gas is heated at constant value until the pressure is doubled and again heated at constant pressure until volume is doubled. The average molar heat capacity for whole process is :-
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1 solution
Let initial pressure, volume, temperature be P' , V' , T' indicated by state A in P-V diagram. The gas is then isochorically taken to state B (2P' , V' , 2T') and then taken from state B to state C (2P' , 2V' , 4T') isobarically .
Total heat absorbed by 1 mole of gas D Q = C V ( 2 T ′ − T ′ ) + C P ( 4 T ′ − 2 T ′ ) 5 R T ′ / 2 + ( 7 R / 2 ) 2 T ′ = 1 9 R T ′ / 2
Total change in temperature from state A to C is D T = 3 T ′
From this we can find molar heat capacity using formula Q / T The answer is 19R/6