Physics Answer Note #71

Question 1 The thermo EMF of a thermocouple varies with the temperature theta of the hot junction as E = a theta + b theta square in volts where a/b = - 700 degree Celsius and cold junction is at 0 degree Celsius calculate the neutral temperature Answer To calculate the neutral temperature in this scenario, we first need to understand the relationship between thermo EMF and temperature theta. According to the given equation, the thermo EMF (E) is directly proportional to temperature theta, with a coefficient of a. Additionally, the coefficient of b represents the quadratic relationship between E and theta, meaning that E increases at a faster rate than theta. In this equation, we are also given the ratio of a/b, which is -700 degree Celsius. This ratio is important because it tells us the relative values of a and b, which in turn affects the shape of the curve between E and theta. With this information, we can now proceed to solve for the neutral temperature. By definition, the neutral temperature is the temperature at which the thermo EMF is zero. Mathematically, this can be represented as E = 0. Plugging this value into the given equation, we get 0 = a theta + b theta square. Since a and b are both negative, we can rewrite the equation as 0 = a theta - |b| theta square. Next, we can factor out theta to get 0 = theta (a - |b| theta). From this equation, we can see that the solution for theta can either be 0 or a/|b|. However, since the cold junction is at 0 degree Celsius, the neutral temperature cannot be 0. Therefore, we can conclude that the neutral temperature in this scenario is a/|b|. To calculate the numerical value, we need to first determine the values of a and b. From the given ratio of a/b = -700 degree Celsius, we can set up the equation a/b = -700 = a/(700 |b|). Solving for b, we get b = a/(-700). Plugging this value into the equation for the neutral temperature, we get a/|b| = a/ (a/(-700)) = -700 degree Celsius. Therefore, the neutral temperature in this scenario is 350 degree Celsius. Question 2 The thermo EMF of a thermao couple varies with the temperature theta and hot Junction as E = 8 theta + b theta square involt where a/b equals to minus 700 degree Celsius and ankol junction is at 0 degree Celsius calculate the neutral temperature Answer The thermo EMF (electromotive force) of a thermocouple is a measurement of the voltage or potential difference generated between its two junctions, called the hot junction and the cold junction. This voltage is directly proportional to the temperature difference between the two junctions, and is given by the formula E = aθ + bθ², where E is the EMF, a and b are constants, and θ is the temperature in degrees Celsius. In this given question, the thermocouple has an a/b ratio of -700°C, which means that for every 1°C change in temperature, the EMF will change by -700μV (microvolts). The ankol junction, or the cold junction, is at 0°C, and the hot junction temperature is denoted by θ. To calculate the neutral temperature, we need to find the value of θ when the EMF is equal to 0. In other words, when there is no potential difference between the two junctions. Therefore, we can set the formula E = 0 and solve for θ as follows: 0 = aθ + bθ² θ = (-b ± √(b² - 4ac)) / 2a, where a = b, b = 8, and c = 0 θ = (-8 ± √(64 - 0)) / (2 x 8) θ = (-8 ± 8) / 16 θ = 0 or -1 Since we are dealing with temperature values, we can discard the negative solution and conclude that the neutral temperature of this thermocouple is 0°C. Question 3 The thermo EMF of a thermal copper varies with the temperature theta and hot Johnson a e = 8 theta + b theta square involt where a/b equals to minus 700 degree Celsius and ankol junction is at 0 degree Celsius calculate the neutral temperature Answer The thermo EMF (electromotive force) refers to the voltage generated by a temperature difference between two dissimilar metals. In this question, we are given the formula for the thermo EMF of a thermal copper, which is represented by a variable "theta" that represents temperature in degrees Celsius. We are also given the values of "a" and "b" which are constant factors. To calculate the neutral temperature, we need to find the point at which the voltage (EMF) is equal to 0. This can be done by setting the given equation equal to 0 and solving for theta. 0 = 8 theta + b theta square involt As we do not have the exact value of "b", we can substitute the given information that a/b equals to minus 700 degrees Celsius. 0 = 8 theta + (-700) theta square involt Now, we have to solve this quadratic equation for theta. We can use the quadratic formula: Theta = (-b ± √(b^2 - 4ac))/(2a) Where a = (-700), b = 8 and c = 0. Plugging in these values, we get: Theta = (-8 ± √(64 + 0))/(2(-700)) = (-8 ± 8)/(-1400) = -16/(-1400) or 0/(-1400) Therefore, the two possible values of theta are 0 and -0.0114. However, since temperature cannot be negative, the neutral temperature is 0 degrees Celsius. Question 4 Give me Some questions about thermodynamics subject to ask my teacher and he becomes inspiring Answer Question: Can you explain the concept of entropy and how it relates to thermodynamics? Response: Entropy is a fundamental concept in thermodynamics that measures the level of disorder or randomness in a system. It is often denoted as S and is related to the number of possible microstates that a system can have. In simple terms, it can be described as the tendency of a system to move from a state of order to a state of disorder through natural processes. In thermodynamics, the second law states that the total entropy of a system and its surroundings will always increase over time. This concept is essential in understanding the behavior and changes of systems in thermodynamics. Question 5 During the synthesis of leucine-glycine from leucine and glycine at 27 °C, thermodynamic functions were measured - the change in enthalpy ΔH = 23.63 kJ•mol-1 and entropy ΔS = 8.32 J•mol-1 •K-1 . Determine the change in Gibbs free energy of this reaction. Answer In order to determine the change in Gibbs free energy (ΔG) of this reaction, we can use the equation ΔG = ΔH - TΔS, where ΔH is the change in enthalpy, T is the temperature, and ΔS is the change in entropy. Using the values provided, we can calculate the change in Gibbs free energy as follows: ΔG = (23.63 kJ•mol-1) - (27 °C)(8.32 J•mol-1•K-1) ΔG = 23.63 kJ•mol-1 - 224.64 J•mol-1 ΔG = 23.40 kJ•mol-1 This indicates that the reaction is thermodynamically favorable, as the change in Gibbs free energy is negative. In other words, the reaction releases energy and is therefore spontaneous.