In the gas equation(P+ a/v²)(v-b)=RT, where T is the absolute tempe

1.	In the gas equation(P+ a/v²)(v-b)=RT, where T is the absolute temperature, P is pressure and V is the volume. what is dimension constant "a" and " b"
Answer» We can add and structure only like quantities. ⇒ Dimensions of P = Dimensions of a/V² ...... (i) and dimension of V = Dimensions of b ............ (ii) From (i), Dimensions of a = Dimensions of P× Dimensions of V² [a] =[M¹ L⁻¹ T⁻² ]×[L³ ]² =[M¹ L⁵ T⁻² ] Unit of a= Unit of p×Unit of v² N/m² \(\times\) m⁶=Nm⁴ From (ii), [b] = [V]=[M⁰ L³ T⁰] So unit of b = Unit of V = m³

In the gas equation(P+ a/v²)(v-b)=RT, where T is the absolute temperature, P is pressure and V is the volume. what is dimension constant "a" and " b"

Answer»

We can add and structure only like quantities.
⇒ Dimensions of P = Dimensions of a/V² ...... (i)
and dimension of V = Dimensions of b ............ (ii)
From (i),
Dimensions of a = Dimensions of P× Dimensions of V² [a]

=[M¹ L⁻¹ T⁻² ]×[L³ ]²

=[M¹ L⁵ T⁻² ]

Unit of a= Unit of p×Unit of v²

N/m² \(\times\) m⁶=Nm⁴

From (ii), [b] = [V]=[M⁰ L³ T⁰]

So unit of b = Unit of V = m³

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In the gas equation(P+ a/v²)(v-b)=RT, where T is the absolute temperature, P is pressure and V is the volume. what is dimension constant "a" and " b"

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