Answer :

Given:


Mass of piston(m) = 50 kg


Area(A) = 100 cm2 = (100x10-4)m2 (since 1m = 100 cm)


Acceleration due to gravity, g = 10 ms-2


Atmospheric pressure = 100 kPa


Distance through which it moves = 20 cm


γ = 1.4


Formula used:


Therefore, pressure exerted by piston = =


= ((50x10)/(100x10-4)) Pa


= 50,000 Pa


Atmospheric pressure = 100 kPa = 1,00,000 Pa.


Therefore, Total pressure(P) = (50,000 + 1,00,000)Pa


=1,50,000Pa


Work done = Pressure x change in volume = P x dV


dV(change in volume) = distance moved by piston x Area


= (20cm x 100cm2)


= 2,000 cm3 = 2,000 x 10-6 m3 = 2 x 10-3 m3


Therefore, Work = (1,50,000 x 2 x 10-3) J = 300 J


Work done, W= P∆V =n R dT


We get,



Now, We calculate Q:


dQ= nCpdt =


Given: γ = 1.4 = . Also,. Solving these two equations, we get Cp = 7R/2, Cv = 5R/2.


Hence, dQ = = 1050 J.


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