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Write the relationship between Permutation and Combination? |
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Answer» Solution :(i)During expansion, work is done by the system, since `V_f > V_i`, the sign obtained for work will be negative (ii) During compression, work is done on the system, since `V_f > V_i`the sign obtained for work will be positive (iii) If the pressure is not constant, but changes during the process such that it is alwaysinfinitesimally greater than the pressure of the gas, then, at each stage of compression, the volume decreases by an infinitesimal AMOUNT, dV. (iv)We can calculate the work done on the gas by the relation, `w=-int_(V_i)^(V_f)PdV`...(1) (v)In a compression process, `P_(ext)` the external pressure is ALWAYS greater than the pressure of the system. i.e... `P_"ext"=(P_"int"+dp)`. In an expansion process, the external pressure is always less than the pressure of the system i.e., `P_"ext"-=(P_"int"-dp)` (v) In general case, we can write, `P_"ext"=(P_"int" pm dp)` . Such processes are called reversible processes.For a compression process, work can be related to internal pressure of the system under reversible CONDITIONS by writing equation . `w="rev"=-int_(V_i)^(V_f) P_"ex"dV=-int_(V_i)^(V_f) (P_"int"pm dP) dV` ....(2) Since dp. dv is very small , we can write `w_"rev"=-int_(V_i)^(V_f)P_"int"dV`....(3) For a given system, `P_"int"V=nRT` `P_"int"V=(nRT)//V` `w_"rev"=-int_(V_i)^(V_f) (nRT)/V dv` ...(4) `w_"rev"=-nRT int_(V_i)^(V_f) (dV)/V` `w_"rev"=-nRT ln (V_f_/V_i)` `w_"rev"=-2.303 nRT log (V_f/V_i)`....(5) (viii) If `V_f > V_i)` (expansion ) , the sign to work done by the process is negative. If `V_f LT V_i` (compression ) , the sign to work done by the process is positive . |
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