Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 18, Problem 94P
To determine
The proof that molar heat capacity is
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A bottle of volume V = 0.15 m³ contains helium gas (a monatomic gas) at a pressure p = 722,266 Pa (Pascal = N/m² and temperature T = 300 K.
Calculate a numerical value for the internal energy U of this gas.
Include units in your answer, using Sl units (m for meters, kg for kilograms, s for seconds, J for joules, K for kelvin, etc.).
Write your answer as an exponential as described in the instructions.
The volume V of an ideal gas varies directly with the temperature T and inversely with the pressure P. If a cylinder of 50 liters contains oxygen at a temperature of 200 K and a pressure of 5 atmospheres, what would the gas pressure be if the volume was changed to 30 liters and the temperature raised to 240 K?
The pressure, volume, and temperature of a mole of an ideal gas are related by the equation
PV = 8.31T,
where P is measured in kilopascals, V in liters, and T in kelvins. Use differentials to find the approximate change in the pressure (in kPa) if the volume increases from 14 L to 14.3 L and the temperature decreases from 325 K to 320 K. (Note whether the change is positive or negative in your answer. Round your answer to two decimal places.)
Chapter 18 Solutions
Physics for Scientists and Engineers
Ch. 18 - Prob. 1PCh. 18 - Prob. 2PCh. 18 - Prob. 3PCh. 18 - Prob. 4PCh. 18 - Prob. 5PCh. 18 - Prob. 6PCh. 18 - Prob. 7PCh. 18 - Prob. 8PCh. 18 - Prob. 9PCh. 18 - Prob. 10P
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- For a temperature increase of 10 at constant volume, what is the heat absorbed by (a) 3.0 mol of a dilute monatomic gas; (b) 0.50 mol of a dilute diatomic gas; and (c) 15 mol of a dilute polyatomic gas?arrow_forwardOne process for decaffeinating coffee uses carbon dioxide ( M=44.0 g/mol) at a molar density of about 14,0 mol/m3 and a temperature of about 60 . (a) Is CO2 a solid, liquid, gas, or supercritical fluid under those conditions? (b) The van der Waals constants for carbon dioxide are a=0.3658 Pa m6/mol2 and b=4.286105 m3/mol. Using the van der Waals equation, estimate pressure of CO2 at that temperature and density. `arrow_forwardOn a hot summer day, the density of air at atmospheric pressure at 35.0C is 1.1455 kg/m3. a. What is the number of moles contained in 1.00 m3 of an ideal gas at this temperature and pressure? b. Avogadros number of air molecules has a mass of 2.85 102 kg. What is the mass of 1.00 m3 of air? c. Does the value calculated in part (b) agree with the stated density of air at this temperature?arrow_forward
- Cylinder A contains oxygen (O2) gas, and cylinder B contains nitrogen (N2) gas. If the molecules in the two cylinders have the same rms speeds, which of the following statements is false? (a) The two gases haw different temperatures. (b) The temperature of cylinder B is less than the temperature of cylinder A. (c) The temperature of cylinder B is greater than the temperature of cylinder A. (d) The average kinetic energy of the nitrogen molecules is less than the average kinetic energy of the oxygen molecules.arrow_forwardOne of a dilute diatomic gas occupying a volume of 10.00 L expands against a constant pressure of 2.000 atm when it is slowly heated. If the temperature of the gas rises by 10.00 K and 400.0 J of heat are added in the process, what is its final volume?arrow_forwardThe ideal gas law relates the pressure P, volume V, and temperature T of an ideal gas: PV = nRT where n is the number of moles and R = 8.3145 J/(K mol). Plots of pressure versus volume at constant temperature are called isotherms. Plot the isotherms for one mole of an ideal gas for volume ranging from 1 to 10 m', at tempera- tures of T = 100, 200, 300, and 400 K (four curves in one plot). Label the axes and display a legend. The units for pressure are Pa. n=1arrow_forward
- The enthalpy of a system is given by the equation H=U+PV where U is the internal energy, P=pressure, and V=volume. In addition, the internal energy, U=Q+W where Q is the heat and W is the work. Suppose we want to find the rate of change in the enthalpy at constant pressure of 1.75 atm, what is the value when heat is absorbed by the system at a rate of 55 J/s and work is done by the system at a rate of 200 J/s when the change of volume is rated at 76 x 10^-5 m^3/s? 1. What is the change in heat with respect to time?2. What is the change in internal energy of the system with respect to time?3. What is the change in enthalpy of the system with respect to time?arrow_forwardEither give an exact answer, or make sure you include at least 4 significant digits on your answer. The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of an ideal gas are related by the equation PV = 8.31T. Find the rate at which the volume is changing when the temperature is 330 K and increasing at a rate of 0.15 K/s and the pressure is 26 and increasing at a rate of 0.03 kPa/s. 1110 L/Sarrow_forwardThe molar heat capacity at constant pressure of carbon dioxide is 29.14 J/K.mol. (a) What is the value of its molar heat capacity at constant volume? J/mol. 4 sig. (b) Calculate the change in enthalpy when 1 mole carbon dioxide is heated from 15°C (the temperature when the air is inhaled) to 37°C (blood temperature, the temperature in our lungs)? number normal format. (c) Calculate molar internal energy when carbon dioxide is heated from 19.16 °C (the temperature when the air is inhaled) to 37°C (blood temperature, the temperature in our lungs). normal format. J/mol 3 sig. number Click Save and Submit to save and submit. Click Save All Answers to save all answers. E R O El 5 G E O A J/K.mol. 4 sig. number H FO 1₂ Save All A 87°F ^!arrow_forward
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