ThermodynamicsHard
Question
Two identical containers A and B with friction pistons contain the ideal gas at the same temperature and the same volume v. The mass of the gas in A is mA and b in mB. The gas in each cylinder is now allowed to expand isothermally to the same final volume 2v. The changes in pressure in a b are found to be ᐃp and 1.5 ᐃp respectively. Then
Options
A.4mA = 9mB
B.2mA = 3mB
C.3mA = 2mB
D.9mA = 4mB
Solution
The initial pressure in the two containers will be
PA =
= mA 
PB =
= mB
After isothermal expasion, pressure will be
P′B =
= mB 
P′A =
= mA 
∴ - ᐃPA = PA - P′A = mA
∴ - ᐃPB = PB - P′B = mB
But ᐃPA = ᐃP and - ᐃPB = 1.5 ᐃ
So,
⇒ - ᐃPA = 
mA
or mA =
∴ 3mA = 2mB
PA =
= mA PB =
= mB After isothermal expasion, pressure will be
P′B =
= mB P′A =
= mA ∴ - ᐃPA = PA - P′A = mA
∴ - ᐃPB = PB - P′B = mB
But ᐃPA = ᐃP and - ᐃPB = 1.5 ᐃ
So,
⇒ - ᐃPA = mA
or mA =
∴ 3mA = 2mB
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