1. Problem 1 - Exact differentials practice. Suppose a function A depends on 3 thermo- dynamics...

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1. Problem 1 - Exact differentials practice. Suppose a function A depends on 3 thermo- dynamics variables, A(N,V,T). (a) Look up the definition of an exact differential and then fill in the following blanks: dA = __dN + ___dV + dT (1) (b) We will learn later that A represents something called the Helmholz free energy, and we will see that: dA-SdT - PdV + d (2) Use what you wrote in (a) to get an expression for S, P, and in terms of the partial derivatives of A with respect to N, V, and T. [Hint, you will find the correct answers if you look up the Helmholz free energy] 2. Problem 2 - Work of expansion of a freezing ice cube. You have an ice cube tray with little divets of size approximately 2 cm x 2 cm x 2 cm. You fill each divet perfectly with water and put it in the freezer. The density of liquid water is 1 g/cm and that of ice is 0.915 g/cm at freezing. Therefore, when the water freezes into ice, and the ice expands slightly outside the divets as you have no doubt seen. (a) Calculate the work change for a single ice cube freezing at constant pressure of 1 atm. (b) Is work done on the system or by the system? (c) Calculate the work for 1 mol of an ideal gas to have the same change in volume at a constant temperature of T = 0C (i.e. not constant pressure). 1. Problem 1 - Exact differentials practice. Suppose a function A depends on 3 thermo- dynamics variables, A(N,V,T). (a) Look up the definition of an exact differential and then fill in the following blanks: dA = __dN + ___dV + dT (1) (b) We will learn later that A represents something called the Helmholz free energy, and we will see that: dA-SdT - PdV + d (2) Use what you wrote in (a) to get an expression for S, P, and in terms of the partial derivatives of A with respect to N, V, and T. [Hint, you will find the correct answers if you look up the Helmholz free energy] 2. Problem 2 - Work of expansion of a freezing ice cube. You have an ice cube tray with little divets of size approximately 2 cm x 2 cm x 2 cm. You fill each divet perfectly with water and put it in the freezer. The density of liquid water is 1 g/cm and that of ice is 0.915 g/cm at freezing. Therefore, when the water freezes into ice, and the ice expands slightly outside the divets as you have no doubt seen. (a) Calculate the work change for a single ice cube freezing at constant pressure of 1 atm. (b) Is work done on the system or by the system? (c) Calculate the work for 1 mol of an ideal gas to have the same change in volume at a constant temperature of T = 0C (i.e. not constant pressure).