The equation fo state of a gas is given by (P+(a)/(V^(3)))(V-b^(2))=cT, where P,V,T are pressure, volume and temperature respectively, and a,b,c are constants. The dimesions of a and b are respectively

The equation fo state of a gas is given by (P+(a)/(V^(3)))(V-b^(2))=c

1.	The equation fo state of a gas is given by (P+(a)/(V^(3)))(V-b^(2))=cT, where P,V,T are pressure, volume and temperature respectively, and a,b,c are constants. The dimesions of a and b are respectively
Answer» <html><body><p>`[ML^(<a href="https://interviewquestions.tuteehub.com/tag/8-336412" style="font-weight:bold;" target="_blank" title="Click to know more about 8">8</a>)T^(-2)] and [L^(3//2)]`<br/>`[ML^(5)T^(-2)] and [L^(3)]`<br/>`[ML^(5)T^(-2)] and [L^(<a href="https://interviewquestions.tuteehub.com/tag/6-327005" style="font-weight:bold;" target="_blank" title="Click to know more about 6">6</a>)]`<br/>`[ML^(6)T^(-2)] and [L^(3//2)]`</p>Solution :Given `[P+(a)/(<a href="https://interviewquestions.tuteehub.com/tag/v-722631" style="font-weight:bold;" target="_blank" title="Click to know more about V">V</a>^(3))](V-b^(2))=cT` <br/> Dimension of `(a)/(V^(3))`=dimension of `<a href="https://interviewquestions.tuteehub.com/tag/pv-593601" style="font-weight:bold;" target="_blank" title="Click to know more about PV">PV</a>^(3)` <br/> `[a]=[(F)/(A)V^(3)]""(becauseP=(F)/(A))` <br/> `=([MLT^(-2)])/([L^(2)])xx[L^(3)]^(3)=[ML^(8)T^(-2)]` <br/> <a href="https://interviewquestions.tuteehub.com/tag/dimensions-439808" style="font-weight:bold;" target="_blank" title="Click to know more about DIMENSIONS">DIMENSIONS</a> of `b^(2)`=dimensions of V <br/> `therefore[b]=[V]^(1//2)=[L^(3)]^(1//2)` or `[b]=[L^(3//2)]`</body></html>