Manipal MET2020PhysicsThermodynamics
Two identical containers A and B with frictionless pistons contain the same ideal gas at the same temperature and the same volume V . The mass of the gas in A is m_A and that in B is m_B . The gas in each container is now allowed to expand isothermally to the same final volume 2 V . The changes in the pressure in A and B are to be found p and 1.5 p respectively, then relation for masses will be
Options
- A4 m_A=9 m_B
- B2 m_A=3 m_B
- C3 m_A=2 m_B
- D9 m_a=4 m_B
Correct answer
C. 3 m_A=2 m_B
Step-by-step solution
For isothermal expansion of an ideal gas p V= constant p V+V p=0 For container A , p_ i A (V)+V( p)=0 p_ i A =- V P V =- p .....(i) where, p_i is initial pressure. For container B , p_ iB (V)+V(1.5 p)=V p_ i B =-1.5 p ....(ii) From Eqs. (i) and (ii), we have p_ i A = p_ i B 1.5 = 2 3 p_ i B m_A= 2 3 m B 3 m_A=2 m B [ p m]