Two identical cylinders, each fitted with a movable piston of the same radius, contain equal number of moles of two different ideal gases. Gas A is monatomic and Gas B is diatomic. Both gases are heated at constant pressure by supplying the same amount of heat Q . If the pistons move outward without friction, what is the ratio of the displacement of the piston for Gas A to that for Gas B ( x_A : x_B )?

Step-by-step solution

For an isobaric process, the heat supplied is Q = n C_p T and the work done by the gas is W = n R T . From these, the work done can be expressed in terms of heat supplied as: W = Q ( R C_p ) For the monatomic gas A , the molar heat capacity at constant pressure is C_ p,A = 5 2 R . Thus, W_A = Q ( R 5 2 R ) = 2Q 5 For the diatomic gas B , the molar heat capacity at constant pressure is C_ p,B = 7 2 R . Thus, W_B = Q ( R 7 2 R ) = 2Q 7 The work done by the gas in moving the piston by distance x is W = P V = P ( r^2)