The application of Euler’s reciprocity relation (cross-derivative rule) to the volume of 1 mole of an ideal gas results in mixed second derivative of V equal to

​For a van der Waals gas, the partial derivative $$\left( \frac{\partial U}{\partial V} \right)_T$$is

​The excess molar entropy of mixing of liquid A with liquid B is -Rln2. The experimentally observed change in entropy upon mixing 1.0 mol of liquid A with 1.0 mol of liquid B is

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The change in chemical potential (in J) of one mole of an ideal gas, when it is compressed isothermally at 300 K from 1.0 atm to 2.0 atm, is closest to (ln2=0.69)

A monatomic perfect gas undergoes expansion from (P₁,V₁) to (P₂,V₂) under isothermal or adiabatic conditions. The pressure of the gas will fall more rapidly under adiabatic conditions because

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​$$\text{1 mole of } ^{16}\text{O}_2 \text{ and 1 mole of } ^{18}\text{O}_2$$ in two different containers of the same volume have the same entropy. Assuming there are no rotational and vibrational contributions to the entropy, if the temperature of $$^{16}\text{O}_2 \text{ is 300 K, what is the temperature of } ^{18}\text{O}_2 \text{ in K?}$$​ 

During the phase transition, at constant temperature, of a solid from one form to another, the change in molar volume, $$\Delta V_m = 1.0\,\text{cm}^3\text{mol}^{-1}$$ is independent of pressure. The change in molar Gibbs free energy, in units of $$J mol^{-1}$$, ​when the pressure in increased from 1 bar to 3 bars is

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The Gibbs free energy of mixing for a regular binary solution of components A and B, at temperature T, on the basis of the Margules equation for activity coefficient, is (in standard notation)

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Among the following, the correct thermodynamic equation of state is

The change in the entropy and the Gibbs free energy of a system are denoted by ΔS and  ΔG , respectively. For reversible melting of ice at 1atm and 0°C,

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The application of Euler’s reciprocity relation (cross-derivative rule) to the volume of 1 mole of an ideal gas results in mixed second derivative of V equal to