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A horizontally kept cylindrical vessel closed at both ends is separated into two equal (42 cm each) parts by an adiabatic piston. Both parts contain gas having equal mass at a temperature of 27^@ C and a pressure of 1 atm. How much should the gas be heated in one part of the cylinder to shift the piston by 2 cm? Find the pressure p of the gas after shifting of the piston. |
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Answer» Solution :Since the gas in both ends is having equal mass and the piston is in equilibrium, ` (V_2)/( V_1)= (T_2)/(T_1)` hence`T_2= (V_2)/(V_1)T_1` Considering I, and I, as the new lengths of the cylinder, ` V_2= pir^2 l_2andV_i = PI r^2l_1` Calculations: CALCULATING`T_2 ` ` T_2 = (V_2)/(V_1) T_i =(l_2 )/(l_1) T_i` `=(44 )/( 40 ) XX 27 ^@C =30 ^@C =330 K` applyingboyle.slawto thevolumeof thegaswhosetemperaturedoesnot change, weobtain ` p= (p_0 V_0)/(V_i)` usingthe values ` P_0 =1atm, V_0= 44 pir^2 ` and`V_i = 42pir^2 `we get ` p = (1 xx 44 pi r^2 )/( 42pir^2 ) = 1.05 atm` |
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