## Temperature Conversions and Thermal Expansion Concepts### Temperature Conversion Formulas1. **Celsius to Kelvin:** \[ T_C = T_K - 273^\circ C \]2. **Celsius to Fahrenheit:** \[ T_F = \frac{9}{5}T_C + 32 \]3. **Fahrenheit to Celsius:** \[ T_C = \frac{5}{9}(T_F - 32) \]### Thermal Expansion1. **Linear Expansion:** \[ \Delta L = \alpha L_0 \Delta T \]2. **Area Expansion:** \[ \Delta A = \gamma A_0 \Delta T \quad \gamma = 2\alpha \]3. **Volume Expansion:** \[ \Delta V = \beta V_0 \Delta T \quad \beta = 3\alpha \]### Gas Laws and Kinetic Theory1. **Ideal Gas Law:** \[ PV = nRT \] - \( P \): Pressure - \( V \): Volume - \( n \): Number of moles - \( R \): Universal gas constant (8.31 J/mole-K) - \( T \): Temperature in Kelvin2. **Combined Gas Law:** \[ \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2} \]3. **Kinetic Energy of Gas Particles:** \[ \frac{1}{2} mv^2 = \frac{3}{2} k_B T \] - \( m \): Mass of a particle - \( v \): Velocity of a particle - \( k_B \): Boltzmann’s constant (\(1.38 \times 10^{-23}\) J/K) - \( T \): Temperature in Kelvin### Constants- **Number of Moles Calculation:** \[ \text{Number of moles, } n = \frac{\text{mass (grams)}}{\text{molecular weight}} \]- **Avogadro's Number:** \[ N_A = **Problem: Calculating Air Pressure Inside a Sealed Car**A certain Volkswagen Beetle is air-tight, so that when the doors are closed and the windows rolled up, no air can escape or enter. Suppose the car is parked with its doors closed and the interior air at an initial pressure of 1.00 atmosphere, and the initial temperature \( T_1 = 22^\circ \text{C} \). Later, due to the greenhouse effect, the temperature rises to \( T_2 = 52^\circ \text{C} \). What will be the air pressure inside the car?---**Explanation:**- This problem involves understanding how temperature changes affect air pressure in a confined space, applying principles of thermodynamics.- You can use the ideal gas law to solve this, assuming the quantity of air and the volume of the car remain constant. Steps:1. Convert temperatures from Celsius to Kelvin by adding 273.15.2. Use the formula: \( P_1/T_1 = P_2/T_2 \) to find the new pressure \( P_2 \).There are no graphs or diagrams included in the original text.

Answered: Image /qna-images/answer/bfb0d63c-225f-4986-b240-4b50c95961f6.jpg

A certain Volkswagen Beetle is air-tight, so that when the doors are closed and the windows rolled up, no air can escape or enter. Suppose the car is parked with its doors closed and the interior air at an initial pressure of 1.00 atmosphere, and the initial temperature Ti = 22,0° C. Later, due to the greenhouse effect, the temperature rises to T2 = 52° C. What will be the air pressure inside the car?

A certain Volkswagen Beetle is air-tight, so that when the doors are closed and the windows rolled up, no air can escape or enter. Suppose the car is parked with its doors closed and the interior air at an initial pressure of 1.00 atmosphere, and the initial temperature Ti = 22,0° C. Later, due to the greenhouse effect, the temperature rises to T2 = 52° C. What will be the air pressure inside the car?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

A weather balloon rises through the atmosphere, its volume expanding from 4.9 m3 to 14 m3 as the temperature drops from 21 ∘C to -10 ∘C. If the initial gas pressure inside the balloon is 1.0 atmatm, what is the final pressure?
A 2.5 L helium balloon is filled at a florist's shop. If the temperature inside the shop is 68°F, what volume will the helium occupy after being left in an automobile at -5°F in the parking lot for the day? ... A -0.18 L В 5.0 L 2.1 L D 1.6 L
People that live at high altitudes often notice that sealed bags of food are puffed up because the air inside has expanded since they were sealed at a lower altitude. In one example, a bag of potato chips was packed at a pressure of 1.00atm and a temperature of 20.5 degrees celcius. The bag was then transported to Santa Fe. The sealed bag of potato chips then finds its way to a summer picnic where the temperature is 31.6 degrees celcius, and the volume of air in the bag has increased to 1.4 times its original value. At the picnic in Santa Fe, what is the pressue, in atmospheres, of the air in the bag?
Suppose you start your day in Denver, on a cool 10°C spring day. The local atmospheric pressure is 85 kPa. You fill your car’s tires until the gauge shows 210 kPa (about 30 psi). You then drive up to Fairplay, Colorado, where the atmospheric pressure is lower—70 kPa—and the temperature drops to 0°C.When you finish lunch, you check your tire pressure. What does the gauge read?
33. A bicycle tire has a pressure of 7.00 × 10° N/m² at a temperature of 18.0°C and contains 2.00 L of gas. What will its pressure be if you let out an amount of air that has a volume of 100 cm³ at atmospheric pressure? Assume tire temperature and volume remain constant.
Internal human body temperature is often stated to be normal at 98.6°F. What is this temperature on the Celsius and Kelvin scales? (b) Gallium boils at 2205°C. What is the corresponding temperature in the Fahrenheit and Kelvin scales? (c) The boiling point of liquid nitrogen is 77.0 K. What is corresponding temperature in the Fahrenheit and Celsius scales?
A Goodyear blimp typically contains 5300 m of helium (He) at an absolute pressure of 1.10 x 10 Pa. The temperature of the helium is 275 K. What is the mass (in kg) of the helium in the blimp? Number Units the tolerance is +/-2%
A hot air balloon uses the principle of buoyancy to create lift. By making the air inside the balloon less dense then the surrounding air, the balloon is able to lift objects many times its own weight. A large hot air balloon has a maximum balloon volume of 2090 m3. a. If the air temperature in the balloon is 54 °C, how much additional mass, in kilograms, can the balloon lift? Assume the molar mass of air is 28.97 g/mol, the air density is 1.20 kg/m3, and the air pressure is 1 atm.
An apartment has the dimensions 16 m by 8 m by 5 m. The temperature is 30°C, and the relative humidity is 51 percent. What is the total mass (in kg) of water vapor in the air in the apartment?
During an all-night cram session, a student heats up a 0.304 liter (0.304 x 10- 3 m3) glass (Pyrex) beaker of cold coffee. Initially, the temperature is 18.3 °C, and the beaker is filled to the brim. A short time later when the student returns, the temperature has risen to 96.9 °C. The coefficient of volume expansion of coffee is the same as that of water. How much coffee (in cubic meters) has spilled out of the beaker?