AP EAMCET202123 Aug 2021Morning ShiftPhysicsThermodynamicsActual
Two containers A and B contain equal volumes of an identical gas at the same pressure and temperature. The gas in container A is compressed to half its original volume isothermally, while the gas in container B is compressed to half its original volume adiabatically. The ratio of the final pressure of gas in container B to that of gas in container A is
Options
- A(2)^ -1
- B( 1 2 )^ -1
- C( 1 1- )^2
- D( 1 -1 )^2
Correct answer
A. (2)^ -1
Step-by-step solution
Given, Initial volume of container A, V_A=V Initial volume of container B, V_B=V Initial pressure in A (p_A )= Initial pressure in B (p_B )=p Let their final volumes be V_A^ =V_B^ = V 2 and their final pressure be p_A^ and p_B^ . As, container A is performing isothermal change aligned & & p_A V_A & =p_A^ V_A / 2 & & p_A^ & =2 p_A aligned and container B is performing adiabatic change array rlrl & & p_B V_B^ & =p_B^ ( V_B 2 )^ & p_B^ & =p_B 2^ array From Eqs. (i) and (ii), we get aligned p_B^ p_A^ & = p_B 2^ p_A 2 p