Kinetic Theory Of Gases Question 84
Question: Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K. The piston of A is free to move, while that B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K, then the rise in temperature of the gas in B is
Options:
A) 30 K
B) 18 K
C) 50 K
D) 42 K
Show Answer
Answer:
Correct Answer: D
Solution:
[d] A is free to move,
Therefore heat will be supplied at constant pressure
$ \
Therefore \Delta Q _{A}=nC _{p}\Delta T _{A} $ ?.(i) B is held fixed,
Therefore heat will be supplied at constant volume.
$ \
Therefore \Delta Q _{B}=nC _{v}\Delta T _{B} $ ?(ii) But $ \Delta Q _{A}=\Delta Q _{B} $ (given)
$ \
Therefore nC _{p}\Delta T _{A}=nC _{v}\Delta T _{B} $
$ \
Therefore \Delta T _{B}=( \frac{C _{p}}{C _{v}} )\Delta T _{A} $
$ =\gamma ( \Delta T _{A} )\text{ }[ \gamma =1.4( \text{diaatomic} ) ] $
$ =( 1.4 )( 30K ) $
$ \
Therefore \Delta T _{B}=42K $
BETA
