Textbook Question
Helium gas with a volume of L, under a pressure of atm and at °C, is warmed until both pressure and volume are doubled. What is the final temperature?
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Ch 18: Thermal Properties of Matter
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 18, Problem 1b
A -L tank contains kg of helium at °C. The molar mass of helium is g/mol. What is the pressure in the tank, in pascals and in atmospheres?
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First, convert the mass of helium from kilograms to grams. Since 1 kg = 1000 g, multiply 4.86 * 10^-4 kg by 1000 to get the mass in grams.
Next, calculate the number of moles of helium using the formula: \( n = \frac{\text{mass}}{\text{molar mass}} \). Use the mass in grams and the molar mass of helium, which is 4.00 g/mol.
Convert the temperature from Celsius to Kelvin using the formula: \( T(K) = T(°C) + 273.15 \). Add 273.15 to 18.0°C to find the temperature in Kelvin.
Use the ideal gas law to find the pressure in pascals: \( PV = nRT \). Rearrange the formula to solve for pressure: \( P = \frac{nRT}{V} \). Use \( R = 8.314 \text{ J/(mol·K)} \) for the ideal gas constant, the number of moles \( n \), the temperature in Kelvin \( T \), and the volume \( V \) in liters converted to cubic meters (1 L = 0.001 m³).
Finally, convert the pressure from pascals to atmospheres using the conversion factor: 1 atm = 101325 Pa. Divide the pressure in pascals by 101325 to find the pressure in atmospheres.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Ideal Gas Law
The Ideal Gas Law is a fundamental equation in physics that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law assumes that the gas behaves ideally, meaning interactions between molecules are negligible.
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Conversion of Units
Conversion of units is essential in physics to ensure consistency and accuracy in calculations. In this problem, pressure needs to be expressed in both pascals and atmospheres. Knowing that 1 atmosphere is equivalent to 101,325 pascals allows for conversion between these units. Proper unit conversion is crucial for interpreting results correctly and comparing them with standard values.
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Molar Mass and Moles Calculation
Molar mass is the mass of one mole of a substance, expressed in grams per mole. To find the number of moles of helium in the tank, divide the mass of helium by its molar mass (4.00 g/mol). This calculation is necessary to apply the Ideal Gas Law, as the number of moles (n) is a key variable in determining the pressure of the gas.
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Related Practice
Textbook Question
A -L tank contains kg of helium at °C. The molar mass of helium is g/mol. How many moles of helium are in the tank?
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Textbook Question
Helium gas with a volume of L, under a pressure of atm and at °C, is warmed until both pressure and volume are doubled. How many grams of helium are there? The molar mass of helium is g/mol.
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Textbook Question
A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains m3 of air at a pressure of atm. The piston is slowly pulled out until the volume of the gas is increased to m3. If the temperature remains constant, what is the final value of the pressure?
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