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PROBLEMS 1. Prove the following equations for a simple compressible system. acu (a) T [+] (b) (32) 2 - - 7 [27 (0)], du/T Әр where a and x are the coefficients of thermal expansion and the isothermal compressibility respectively. for a simple compressible system

PROBLEMS 1. Prove the following equations for a simple compressible system. acu (a) T [+] (b) (32) 2 - - 7 [27 (0)], du/T Әр where a and x are the coefficients of thermal expansion and the isothermal compressibility respectively. for a simple compressible system

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PROBLEMS 1. Prove the following equations for a simple compressible system: ace (b) ap = -T (a) = T aT IT where a and k are the coefficients of thermal expansion and the isothermal compressibility respectively. 2. Prove the following equations for a simple compressible system: aT (a) du = C, dT + dv (b) dh= c, dT + (v – aTv) dp %3D KCy (c) ds = aT dp + (d) da=-(opv + s) dT + kpv dp dv %3D 3. Find the coefficient of thermal expansion a and the isothermal compressibility k from each of the following p-v-T relations: RT (a) Ideal gas equation, p = %3D RT (b) Dieterici equation, p = v -6 RT (c) Saha-Bose equation, p = e-a/RTV %3D -2b In (2) 2b In the above equations R is the gas constant and a and b are specific constants. Verify that for large values of T and v all the expressions for a and K go over into the corresponding expressions for an ideal gas.
Transcribed Image Text:PROBLEMS 1. Prove the following equations for a simple compressible system: ace (b) ap = -T (a) = T aT IT where a and k are the coefficients of thermal expansion and the isothermal compressibility respectively. 2. Prove the following equations for a simple compressible system: aT (a) du = C, dT + dv (b) dh= c, dT + (v – aTv) dp %3D KCy (c) ds = aT dp + (d) da=-(opv + s) dT + kpv dp dv %3D 3. Find the coefficient of thermal expansion a and the isothermal compressibility k from each of the following p-v-T relations: RT (a) Ideal gas equation, p = %3D RT (b) Dieterici equation, p = v -6 RT (c) Saha-Bose equation, p = e-a/RTV %3D -2b In (2) 2b In the above equations R is the gas constant and a and b are specific constants. Verify that for large values of T and v all the expressions for a and K go over into the corresponding expressions for an ideal gas.
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