Physics Answer Note #68

Question 1 Question 1 Write the following dimensions in SI units: 1)Height of the cylinder 8.0 cm 2)Diameter of the cylinder 1.0 cm 3)Mass of the cylinder 18.9 g 4)What is the radius of the cylinder in cm? 5)What is the radius of the cylinder in SI units Question 2 Calculate the volume of the cylinder in cm^3 Question 3 Calculate the volume of the cylinder in m^3 Question 4 Calculate the density of cylinder in g/cm^3 Question 5 Calculate the density of cylinder in kg/m^3 Question 6 Write the following dimensions in SI units 1) Length of the block 5.1 cm 2)Width of the block 3.9 cm 3)Height of the block 1.9 cm 4)Mass of the block 319.7 g Question 7 Calculate the volume of the block in cm^3 Question 8 Calculate the volume of the block in m^3 Question 9 Calculate the density of the block in g/cm^3 Question 10 Calculate the density of the block in kg/m^3 Question 11 Write the following dimensions in SI units 1. Mass of empty container 85.2 g 2. Mass of container and water 145.4 g 3. Volume of water 61 ml 4. Mass of water in grams 5. Mass of water in SI units Question 12 Calculate the density of water in g/cm^3 Question 13 Calculate the density of water in kg/m^3 Conclusion Question 14 The density of the object A (the cylinder) is experimentally determined as (give value)…………. , which compares well with the value(s) of (give value(s) from the table)……………….. Therefore object A (the cylinder) is identified as substance made of …………………….. Question 15 The density of object B (the rectangular block) is experimentally determined as (give value)……………………, which compares well with the value(s) of (give the values from the table)…………………... Therefore object B is identified as substance made of ………………………… Question 16 The density of water is experimentally determined as……………………. This value compares well/not well with the value of (give value from the table)……………………….. Question 17 Suggest 3 reasons why your experimental values differ from the values in the table. Answer 1) Height of the cylinder: 8.0 cm = 0.08 m. (1 cm = 0.01 m) 2) Diameter of the cylinder: 1.0 cm = 0.01 m. (1 cm = 0.01 m) 4) Radius of the cylinder in cm = 0.5 cm. (radius = diameter/2) 5) Radius of the cylinder in SI units = 0.005 m. (1 cm = 0.01 m) Calculate the volume of the cylinder in cm^3 To calculate the volume of the cylinder, we first need to find the area of the base, which is given by the formula: A = πr^2 (where r is the radius of the cylinder). Substituting the given value, we get: A = 3.14 x (0.5 cm)^2 = 0.785 cm^2 Now, we can calculate the volume using the formula: V = Ah (where A is the area of the base and h is the height of the cylinder). Substituting the given values, we get: V = (0.785 cm^2)(8.0 cm) = 6.28 cm^3 Therefore, the volume of the cylinder is 6.28 cm^3. Calculate the volume of the cylinder in m^3 To calculate the volume of the cylinder in m^3, we first need to convert the given dimensions to meters (since volume is measured in m^3). Height of the cylinder = 0.08 m Radius of the cylinder = 0.005 m Using the same formula as above, we get: V = (π)(0.005 m)^2(0.08 m) = 3.14 x 0.000025 x 0.08 m^3 = 0.00000628 m^3 Therefore, the volume of the cylinder in m^3 is 0.00000628 m^3. Calculate the density of the cylinder in g/cm^3 The density of a substance is given by the formula: ρ = m/V (where ρ is density, m is mass, and V is volume). Substituting the given values, we get: ρ = (18.9 g)/6.28 cm^3 = 3.01 g/cm^3 Therefore, the density of the cylinder is 3.01 g/cm^3. Calculate the density of the cylinder in kg/m^3 To calculate the density in kg/m^3, first we need to convert the given values to the corresponding SI units. Mass of the cylinder = 0.0189 kg Volume of the cylinder = 0.00000628 m^3 Now, using the same formula as above, we get: ρ = (0.0189 kg)/0.00000628 m^3 = 3012 kg/m^3 Therefore, the density of the cylinder in kg/m^3 is 3012 kg/m^3. Write the following dimensions in SI units 1) Length of the block 5. Question 2 Provide the specification of thermal sensor and give the practical application of it in points Answer A thermal sensor, also known as a temperature sensor, is a device that measures temperature by converting thermal energy into an electrical signal. The measurement range, accuracy, response time, and other specifications of a thermal sensor vary depending on its type and usage. In this answer, we will discuss the general specifications of a thermal sensor and provide some practical applications for it. Specification of Thermal Sensor: 1. Measurement Range: The measurement range of a thermal sensor is the lowest and highest temperature values it can accurately measure. It is usually measured in degrees Celsius (°C) or Fahrenheit (°F). The range can vary from a few degrees below freezing to several hundred degrees Celsius, depending on the type of thermal sensor. 2. Accuracy: The accuracy of a thermal sensor is the degree of closeness between the measured temperature and the actual temperature. It is expressed in degrees Celsius (°C) or Fahrenheit (°F) and is usually given as a fixed error (±) or a percentage of the reading (% of reading). For a high-precision thermal sensor, the accuracy can be as low as ±0.1°C. 3. Response Time: The response time of a thermal sensor is the time taken by the sensor to detect and report a change in temperature. It is typically measured in milliseconds (ms) and depends on the sensor's physical properties, such as thermal mass and thermal conductivity. 4. Resolution: The resolution of a thermal sensor is the smallest change in temperature that it can detect and measure. It is usually given in degrees Celsius (°C) or Fahrenheit (°F) and is directly related to the sensor's accuracy. 5. Calibration: To ensure accuracy and reliability, a thermal sensor needs to be calibrated regularly. Calibration is the process of adjusting the sensor's output to match a known temperature reference. The frequency of calibration can vary from once a year to once every few months, depending on the type and usage of the thermal sensor. Practical Applications of Thermal Sensor: 1. Environmental Monitoring: Thermal sensors are widely used in weather stations, HVAC systems, and other environmental monitoring applications to measure air, water, and soil temperature. 2. Industrial Processes: In industrial settings, thermal sensors are used to monitor the temperature of equipment and processes to ensure that they are operating within safe and optimal temperature ranges. 3. Medical Applications: Thermal sensors are used in medical devices to monitor body temperature, especially for patients in critical care. They are also used in non-contact infrared thermometers for quick and accurate temperature measurements. 4. Automotive Industry: In the automotive industry, thermal sensors are used for engine monitoring, exhaust gas temperature measurement, and cabin temperature control. 5. Food Safety: Thermal sensors play a crucial role in ensuring food safety by monitoring the temperature of refrigerators and freezers in food storage facilities, as well as during transportation. Question 3 why electrons move from higher temperature to lower temperature in see beck effect? Answer The phenomenon of Seebeck effect is a thermoelectric effect that occurs when there is a temperature difference between two ends of a conductive material. This effect results in the generation of an electrical potential and a flow of current in the material. One of the key aspects of Seebeck effect is the movement of electrons from a higher temperature region to a lower temperature region. This movement of electrons is essential for the generation of an electrical potential and current in the material. The movement of electrons from a higher temperature to a lower temperature is based on the principle of energy transfer. According to the second law of thermodynamics, heat flows in the direction of decreasing temperature. In simpler terms, heat always moves from a higher temperature region to a lower temperature region. This is because the energy at a higher temperature is more disordered and has a greater tendency to become more ordered at a lower temperature. As a result, the electrons in the high temperature region have a higher energy and tend to move towards a region with a lower energy, which is the lower temperature region. When a conductive material experiences a temperature difference between its two ends, it results in a flow of heat from the higher temperature region to the lower temperature region. Due to this flow of heat, the energy of the electrons in the high temperature region decreases, creating a thermal gradient. In response to this gradient, the electrons move from the higher temperature region to the lower temperature region, creating a flow of current. This phenomenon of the movement of electrons from a high temperature to a lower temperature is known as the Seebeck effect. The Seebeck effect is widely used in thermoelectric devices, such as thermocouples, to generate electricity from a temperature difference. The Seebeck coefficient, which is a measure of the strength of the Seebeck effect, is an important parameter in the design of these devices. This coefficient is influenced by factors such as the material's composition and temperature. It is also important to note that the Seebeck effect is reversible, meaning that it can also be used to generate a temperature difference from an applied electrical potential. Question 4 A hot plate of surface area 0.025 m2 is placed in an environment of temperature 20 °C. a. The hot plate exchanges energy with the environment at a net rate of 50 W. Calculate the temperature of the hot plate. b. Determine the additional power that must be delivered to the hot plate to increase its temperature to 200 °C. Answer a. To calculate the temperature of the hot plate, we can use the formula for thermal equilibrium: Q = mcΔT, where Q is the heat energy exchanged, m is the mass of the hot plate, c is the specific heat capacity of the hot plate material, and ΔT is the change in temperature. First, we need to calculate the heat energy exchanged using the given net rate of 50 W: 50 W = Q/t, where t is the time in seconds. Assuming that the hot plate has been in contact with the environment for a certain time, we can use any time value in seconds for t. For simplicity, let's use t = 1 second. Therefore, Q = 50 J. Next, we need to determine the mass and specific heat capacity of the hot plate material. Assuming the hot plate is made of aluminum (Al), we can find its specific heat capacity in most Physics textbooks or online sources. According to the National Institute of Standards and Technology, the specific heat capacity of aluminum is 0.897 J/g°C or 897 J/kg°C. Since we do not know the mass of the hot plate, let's assume it as 1 kg for calculation purposes. Plugging in all the values in the formula: 50 J = (1 kg)(897 J/kg°C)(T - 20°C) T = 50.056 °C Therefore, the temperature of the hot plate is approximately 50.056 °C. b. To determine the additional power that must be delivered to the hot plate to increase its temperature to 200 °C, we can use the same formula for thermal equilibrium. Q = mcΔT The final temperature (T) is 200 °C, and the initial temperature is 50.056 °C (calculated in part a). Therefore, ΔT = 200 °C - 50.056 °C = 149.944 °C. Again, using the same values for mass and specific heat capacity of aluminum: Q = (1 kg)(897 J/kg°C)(149.944 °C) Q = 134742.168 J To increase the temperature of the hot plate to 200 °C, an additional heat energy of 134742.168 J or 134.742 kJ is needed. Question 5 A sphere of radius R has an absolute temperature T and it radiates power P. A second sphere has a radius 2R. The spheres can be assumed to be black-body radiators. Determine: a. the power radiated by the second sphere, when its absolute temperature is T b. the absolute temperature of the second sphere, when it radiates power P. Answer a. The power radiated by any black-body radiator is given by the Stefan-Boltzmann Law, which states that the power radiated is directly proportional to the fourth power of the absolute temperature T and the surface area of the radiator A. Mathematically, this can be written as P = σAT^4, where σ is the Stefan-Boltzmann constant. In this case, the first sphere with radius R has a power of P1 = σπR^2T^4. Since the second sphere has a radius of 2R, its surface area would be four times larger, making its power P2 = σπ(2R)^2T^4 = 4P1. Therefore, the power radiated by the second sphere when its absolute temperature is T is 4P1 or 4 times the power of the first sphere. b. To determine the absolute temperature of the second sphere, we can use the inverse of the Stefan-Boltzmann Law. This is known as the Wien's Displacement Law, which states that the wavelength at which the radiated power is maximum is inversely proportional to the absolute temperature. Mathematically, this can be written as λmax = b/T, where λmax is the wavelength at which the radiated power is maximum and b is Wien's displacement constant. In this scenario, we know that the power P2 is equal to P, so we can equate the two forms of the Stefan-Boltzmann Law and solve for the absolute temperature T2 of the second sphere: P = σπ(2R)^2T2^4 P = 4σπR^2T^4 T2^4 = 4T^4 T2 = 2T Therefore, the absolute temperature of the second sphere when it radiates power P would be twice the temperature T of the first sphere.