Q4. Determine the mixture pressure at its equilibrium state.

Part II (10%) Pleasc answer the following question. 31.對公開金鑰加密器RSA而言,選擇一個隨機的大質數一直是基本的問題,在過去是先選擇一個隨機大整數,然後使用Miller-Rabin primalitytesting 演算法去測試此整數是否為質數。在2002年Agrawal, Kayal, and Saxena 提出了另一個演算法(簡稱 AKS演算法)for primality testing 請問若有兩個隨機大整數各自通過這兩個質數測試演算法,在意義上有何不(請說明理由)?(5分)。另請寫出 Miller-Rabinprimaltstng 演算法(Pseudocode)(5分)

Q1. Estimate the mole number of cach gas species in the container.

Q2. If the partition in the box is removed and a heat loss takes place during the mixing process, how do you simplify the 1st law below to evaluate the mixture temperature at its equilibrium state? The first law of thermodynamics for transient processes is expressed as:Subscripts 1 and 2 are states; subscripts i and o are inlet and outlet, respectively.

Q3. Using the simplified equation to calculate the mixture temperature at its equilibrium state.

Problem 2. Complete the questions below (16%; 8 pts each): Q1. To estimate the steady-state heat transfer rate of the liquid-to-steam in the serpentine pipe shown below, how do you simplify the law of thermodynamics in Problem 1-Q2 to do the estimation?

Q2. The questions below are relevant to the humidity in the air conditioning: Q2-1. In the equation of the humidity ratio, ω= mv/ma = 0.622*Pv /(P-Pv), what are P . and Pv, my and ma?Q2-2. In the equation of the relative humidity, RH = Pv /Pg, what is Pg? How can Pg be obtained?

Q1. Sketch the temperature of the ice cube versus time, as it, solely exposed to air at a room temperature, slowly turns from a solid state to a complete liquid state.

Q2. The project is based on a problem that an insulated container is partially filled with a liquid in gas at an isothermal condition where the fluid temperature is higher than the ice temperature. Then, several ice cubes are dropped into the container (see the image below). Regarding this transient process of heat transfer, you are asked to develop a formula based on the first law of thermodynamics to predict the needed ice mass or needed ice initial temperature to achieve a targeted final temperature at its thermal equilibrium. Assuming that you know the liquid mass, liquid temperature, gas mass, gas temperature and thermodynamics properties of liquid, gas and ice. To simplify the analysis, let us assume that the mass of gas remains unchanged after the addition of ice to the container and the process of heat transfer in the container is isobaric. To derive a practical cquation for the analysis described herein, how do you make assumptions and simplify the first law of the thermodynamics based on the equation shown in Problem 1-Q2? List the notations for each parameter and variable in the equation proposed by you.

Q1. Identify the processes by numbers where the heat addition, heat rejection, compression and expansion are involved in one cycle.

Q2. Using the first law of thermodynamics to derive equations for each term in Q1 in terms of the gas temperature.