A monoatomic ideal gas, initially at temperature T?, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T? by releasing the piston suddenly. If ?? and ?? are the lengths of the gas column, before and after the expansion respectively, then the value of T?/T? will be :
A monoatomic ideal gas, initially at temperature T?, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T? by releasing the piston suddenly. If ?? and ?? are the lengths of the gas column, before and after the expansion respectively, then the value of T?/T? will be :
Option 1 -
ℓ₁ / ℓ₂
Option 2 -
(ℓ₂ / ℓ₁)²ᐟ³
Option 3 -
(ℓ₂ / ℓ₁)²ᐟ³
Option 4 -
(ℓ₁ / ℓ₂)²ᐟ³
Asked by Shiksha User
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1 Answer
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Correct Option - 4
Detailed Solution:For adiabatic process
T? V? ¹ = T? V? ¹
⇒ T? (Al? )? ¹ = T? (Al? )? ¹
T? /T? = (l? /l? )? ¹ = (l? /l? )? /³? ¹ = (l? /l? )?
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