The equation of state for a real gas at high temperature is given by P = (nRT/V - b) - - Physics - Units And Measurements

Question

The equation of state for a real gas at high temperature is given
by P = (nRT/V - b) - a/T1/2V(V + b) where n, P, V &
T are the number of moles, pressure, volume & temperature
respectively & R is the universal gas constant Find the
dimensions of constant a in the above equation

Vipra Mishra · Accepted Answer

Dear Student,
Equation given by you can be simplified as

Vander Waal's equation for gas is given byP+naV2V-nb=nRTP is pressure, V is volume and T is temperature
 [P] = [FA]  = [MLT −2L2] = [ML−1T −2] [V] = [L3]Now, From the principle of homogeneity of dimensions,we have∴P=aV2⇒a=PV2=ML-1T-2L32=ML5T-2

Regards,

The equation of state for a real gas at high temperature is given by P = (nRT/V - b) - a/T1/2V(V + b) where n, P, V & T are the number of moles, pressure, volume & temperature respectively & R is the universal gas constant. Find the dimensions of constant a in the above equation.

The equation of state for a real gas at high temperature is given by P = (nRT/V - b) - a/T^1/2V(V + b) where n, P, V & T are the number of moles, pressure, volume & temperature respectively & R is the universal gas constant. Find the dimensions of constant a in the above equation.