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# if pv=k , p/T=k why pv/T=k?

p means intensity of pressure

v means volume

T means absolute temperature

k is any real number

### 1 Answer

- anil bakshiLv 71 decade agoFavorite Answer
PV = k means the process is being carried out so slowly that (take compression case) at every point (P,V) all the heat generated in cylinder goes out to surrounding - so that temp (T) of gas does not vary - T =constant >>> PV = RT=constant- It is called Isothermal process. Everywhere on P-V diagram the product of P and V will remain constant k , which will be determined by that T which is desirably kept constant.

This graph PV = k is xy=c^2 a rectangular hyperbola with asymptotes as axes.

P/T = k1 it indicates that the process is carried out in such a manner that the piston is not allowed to move ie dV = 0 isochoric process. Here weights are kept on /removed from piston in step with heat supplied - because when heat input is given T >>> increases >>>>P increases which attempts to increase V as well. But it kept constant. This on P-V diagram will be a straight line parallel to P-axis or perpendicular to V-axis

PV/T = R this is universally constant ratio - all varying no constraint on P V T therefore they all will vary in such a ratio so as to equate to gas constant.

what you have written k in all 3 equs is wrong there are k , k1 R=8.3 (k depends on T say 300 K -sink temp or .....

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