KTGHard
Question
A thermally insulated chamber of volume 2V0 is divided by a frictionless piston of area S & mass m into two equal parts A and B.Part A has an ideal gas at pressure P0 and temperature T0 and in part B is vacuum. A massless spring of force constant K is connected with the piston and the wall of the container as shown. Initially the spring is undeformed. The gas in chamber A is allowed to expand. Let in equilibrium the spring is compressed by x0 . Then :
Options
A.Pressure of the gas at equilibrium is 
B.Work done by the gas is 
C.Increase in internal energy of the gas is
D.Increase in internal energy of the gas is
Solution
Temperature of the gas is decreased
(A) (D)
For equilibrium of piston
PS = Kx0
P =
For piston
Wall = KE2 − KE1
Wgas −
kx2 = 
mv2
Wgas =
kx2 + mv2 = position
ᐃQ = 0
ᐃQ = ᐃU + W
ᐃU = − W = negative
As internal energy of gas decreases ∴ temperature of gas decreases.
(A) (D)
For equilibrium of piston
PS = Kx0
P =
For piston
Wall = KE2 − KE1
Wgas −
kx2 = mv2Wgas =
kx2 + mv2 = positionᐃQ = 0
ᐃQ = ᐃU + W
ᐃU = − W = negative
As internal energy of gas decreases ∴ temperature of gas decreases.
Create a free account to view solution
View Solution FreeMore KTG Questions
If a container is filled with the mixture of H2 and O2 then :-...The root mean square speed of hydrogen molecules of an ideal hydrogen gas kept in a gas chamber at 0oC is 3180 m/s. The ...The expansion of an ideal gas of mass m in volume at a constant pressure P is given by the straight line B. Then the exp...For a gas sample with N0 number of molecules, function N(V) is given by : N(V) = for 0 < V < V0 and N(V) = 0 for V...A balloon contains 500 m3 of helium at 27o0C and 1 atmosphere pressure. The volume of the helium at - 3oC temperature an...