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Calculate the work done by the torque. |
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Answer» Solution :(i)The essential condition of expansion or compression of a system is there should be difference between external pressure `(P_"ext")` and internal pressure `(P_"int")` (ii)If the volume of the system is increased against the external pressure, the WORK is done by the system. By convention work done by the system is given a negative sign (-W). (iii) If the volume of the system decreased, the work is done on the system. By convention work done on the system is given positive sign (+W). (iv) For understanding pressure-volume work, let us CONSIDER a cylinder which contains one MOLE of an ideal GAS fitted with a frictionless piston. Total volume of the gas is V and pressure of the gas inside is `P _"int"`. (v)If external pressure is `P_"ext"`which is greater than `P_"int"` Piston is moved i want till the pressure inside becomes equal to `P_"ext"`.It is achieved in a single stepand the finalvolume be `V_f`. (vi)During this compression, piston moves a distance (x) and is cross-sectional area of the piston is A, then, Change in volume = `xA =DeltaV =V_f -V_i` ...(1) `P_"ext"="Force(F)"/"Area (A)"`....(2) `therefore F=P_"ext" A` (vii) If work is done by the system by pushing out the piston against external pressure `(P_"ext")`, then according to the equation, -w=F. x ...(3) -w=`P_"ext".A . x`...(4) -w=`P_"ext".DeltaV`...(5) `-w=P_"ext" (V_f-V_i)` ....(6) Simply `w=-P DeltaV`...(7) (viii)From the above equation, we can predict the sign of work (w). (ix) During expansion,work is done bythe system, since `V_f > V_i` , the sign obtained for workwill be negative. (x)During compression, work is done on the system, since `V_f ltV_i` , the sign obtained for work will be positive. 
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