IIT JEE , AIEEE Forum - Physics , Thermal Physics

doucmecomin

coefficient of volume expansion given by

=(dv)/v(dT)

coeff. of vol exp. for ideal gas where pressure is constant is:

a1/T

b2/T

c-1/T

d -2/ T

doucmecomin

THE ANS IS 1/T

hash_include

$gamma = rac {dV}{V.dT}$
also,
$PV = nRT$ ..... (1)
$=> P.dV = nR.dT$
$=> rac {dV}{dT} = rac {nR}{P}$

so,
$gamma = rac {nR}{PV}$
but, from (1), $rac {nR}{PV} = rac 1 T$
so, $gamma = rac 1 T$
Smile

Note that T is the initial temperature.

ashwinigf

nRt/v=k(constant)

v=nrt/k

dv=nrdt/k

dv/v(dt)=nrdt(k)/nrt(k)(dt)

=1/t

so coeff of vol expansion=1/t

doucmecomin

what is wrong in my method ???

= dV/v(dT)

v(dT) = dV

nRT(dT)/P = dV

nRT(dT)/P =

dV

nRT²/2P = V

nRT²/2P = nRT/P

= 2/T

doucmecomin

please someone do tell what is wrong in my method

doucmecomin

please some one tell me where i hv done wrong in my above posted solution i need to know what is wrong in my procedure please reply
rates assured

doucmecomin

please some one tell me where i hv done wrong in my above posted solution i need to know what is wrong in my procedure please reply
rates assured

hash_include

you've not integrated between any limits at all..
i.e. you have to include constants of integration also Smile

eistien

you have not included the constant of integration but if you consider for the case T to vary from T to 2T and V to vary from V to 2V accordingly (from charles law) you get the answer to be gamma=1/T

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