Question

An ideal monatomic gas is contained in a vessel of constant volume 0.470 m3. The initial temperature and pressure of the gas are 300 K and 5.00 atm, respectively. The goal of this problem is to find the temperature and pressure of the gas after 30.0 kJ of thermal energy is supplied to the gas.

(a) Use the ideal gas law and initial conditions to calculate the number of moles of gas in the vessel. mol

(b) Find the specific heat of the gas. J/K

(c) What is the work done by the gas during this process? kJ

d) Use the first law of thermodynamics to find the change in internal energy of the gas. kJ

(e) Find the change in temperature of the gas. K

(f) Calculate the final temperature of the gas. K

(g) Use the ideal gas expression to find the final pressure of the gas. atm

Answer 1

Ang a curen Ujue 0.470 m3 A Te - 3ook, Pi - 5 atm=5* - Pe=5.065X105 pa. A = 30kg = 30x103 J. 1.0138105 pa @ from ideal gas lame :- - PV = nRT Here Pressure, v R * Ceas constant, & volume, n=no. of mole. T - temperature. na PV - Pi Vi - (5.065x105pa) (0.470 mi) R TC 18.314 J/molok) (Book) RT in- 95.44 moles | n = 95.44 moles) Ang calculate specific heat of gas - C = 3 R = 3 X (8.314/mol. x) = 12.471 J/molok Ang © Work done by gas is zero because 2 volume is constant. W205 Ang @ from first lame of AU - AQ+hto AU = 30 kJ / Are thermoely namico oro T- • AU = nCvAT

DATE DATE DIDI AU ncy = 30x1035 (95.44 moles) (12.471 Imolik) AT = 25.205k Ars 0 calculate final temperature of gas" Tt = ATT Ti DT = Tf - Te » It = 25.205k + 300k or If = 325.205k from ideal gas Are lawet @ Pe V = nRTs Pf = nR Tt or Pe=195.44 moles) (8.314 Jmol.k) 1325.205k) Co. 470 m3) . = 549034.gg fa a 54 9035 pallatm TDI 3X05 pe or Pf 25.419 atm ar Ipf = 5.42 atm Au PAGE