A nearly flat bicycle tire becomes noticeably warmer after it has been pumped up. Approximate this process as a reversible adiabatic compression. Assume the initial pressure and temperature of the air before it is put in the tire to be
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Thermodynamics, Statistical Thermodynamics, & Kinetics
- The Dieterici equation of state for one mole of gas is p=RTe-aVRTV-b Where a and b are constants determined experimentally. For NH3g, a = 10.91 atm. L2 and b = 0.0401 L. Plot the pressure of the gas as the volume of 1.00 mol of NH3g expands from 22.4 L to 50.0 L at 273 K, and numerically determine the work done by the gas by measuring the area under the curve.arrow_forwardWhat are the numerical values of the heat capacities c-v and c-p of a monatomic ideal gas,in units of cal/mol.K and L.atm/mol.K?arrow_forwardWhat is the change in internal energy when a gas contracts from 377mL to 119mLundera pressure of 1550 torr, whileat the same time being cooled by removing 124.0J ofheat energy?arrow_forward
- A chemical reaction takes place in a container fitted with a piston of cross-sectional area 50 cm2. As a result of the reaction, the piston is pushed out through 15 cm against an external pressure of 1.0 atm. Calculate the work done by the system.arrow_forwardCalculate the value of cp at 298 K and 1 atm pressure predicted for Cl, and NO, by the classical equipartition theorem. (Enter your answers to at least two decimal places.) Cp(Cl)) = J mol 1 K1 Cp(NO,) = J mol K1 The actual heat capacities of C and NO, are 33.91 and 36.97 J molK, respectively. Calculate the fraction (expressed as a percentage) of the measured value that arises from vibrational motions. vibrational contribution to cp(Cl,) = vibrational contribution to cp(NO,) =arrow_forwardAn ideal monatomic gas expands adiabatically from 0.500 m3 to 1.57 m3. If the initial pressure and temperature are 1.30 ✕ 105 Pa and 350 K, respectively, find the number of moles in the gas, the final gas pressure (Pa), the final gas temperature (in K), and the work done on the gas (in J).arrow_forward
- One mole (1.0 mol) of an ideal gas is initially at T1 = 298 K and has volume V1 = 2.0 L. It is then reversibly expanded to final volume V2 = 3.0 L. Assume Cp = 5/2 R and Cv = 3/2R. a) Calculate the following if the expansion is adiabatic: 1) ΔT 2) q 3) w 4) ΔU 5) ΔHarrow_forwardA gas can expanding adiabatically might stop expanding either because it has filled a rigid container (known final volume) or it has equilibrated with an external pressure (known final volume). Derive the expression for the final pressure of an ideal gas after an adiabatic expansion. Begin with the simple expression derived using the ideal gas law: PiVi Ti Pf Vf Tf Then use the expression for the ratio of the final temperature R/C₂ The final expression is Ti Tf = = (1) Pf = Pi - (² *arrow_forwardA sample of an ideal gas undergoes the cycle A to B to C to D to A. depicted below. All four steps of the cycle can be considered reversible processes. For this gas, Cv=1.5R. There are no properities of gas here. All the information is provided on the graph. Calculate q, w, deltaU, deltaH, deltaS for each step and for the entire cycle. Please clearly label and box your answers in the form of a table. Hint: Start by calculating the number of molesarrow_forward
- Recall that the van der Waals equation of state—an extension of the ideal gas equation—attempts to better capture the behavior of real gases. It can be written to parallel the PV = nRT form of the ideal gas equation: (P + an2/V2) (V − nb) = nRTa) For one mole of a van der Waals gas, derive an expression for the work done by a reversible and isothermal change in volume. In other words, evaluate the following integral for the van der Waals gasw = − {integral with limits from v1 to v2} PdV.b) What are physical interpretations of the van der Waals constants a and b?c) If for helium, the van der Waals constant b is equal to 2.43 × 10–5m3 mol-1, using this value for b, calculate the diameter of the helium atom.arrow_forwardOne mole of nitrogen (N2) is cooled from an initial temperature and pressure of 700 K and 10 bar to a final temperature of 300 K. The heat capacity of nitrogen may be taken as: Cp,m = 28.58 + 3.77 × 10-3 T where Cp,m is in J mol-1 K-1 and T is in Kelvin. Assuming nitrogen behaves as an ideal gas, calculate q, w, ∆U, and ∆H for this process when it is carried out (a) at constant pressure, and (b) at constant volume. Compare the values obtained for the two cases.arrow_forwardYou have four samples of ideal gas, each of which contains the same number of moles of gas and has the same initial temperature, volume, and pressure. You compress each sample to one-half of its initial volume. Rank the four samples in order from highest to lowest value of the final pressure. (i) A monatomic gas compressed isothermally; (ii) a monatomic gas compressed adiabatically; (iii) a diatomic gas compressed isothermally; (iv) a diatomic gas compressed adiabatically.arrow_forward
- Principles of Modern ChemistryChemistryISBN:9781305079113Author:David W. Oxtoby, H. Pat Gillis, Laurie J. ButlerPublisher:Cengage LearningPhysical ChemistryChemistryISBN:9781133958437Author:Ball, David W. (david Warren), BAER, TomasPublisher:Wadsworth Cengage Learning,