1. 10 molecules of an ideal gas do 5 kJ of work on its surroundings as they expa
ID: 1578571 • Letter: 1
Question
1. 10 molecules of an ideal gas do 5 kJ of work on its surroundings as they expand isothermally to a final pressure of 1.75 atm and volume of 18.0L. Determine: (a) The temperature of the gas? (b) The initial volume? NOTES 1 atm-1.01 x 10 Pa, R-8.31 J/(mol-K), NA-6.02x103 molecules/mol - SI unit for volume is m - Prefix "kilo" means "1000 times" - Care should be taken when applying formulas (e.g., the statement "work on its surrounding" has a specific meaning in relation to the formulas) - If you get stuck consider whether ideal gas equation might come to the rescue 2. 22.50 g of helium are heated from 20°C to 90°C in a 2.50 L sealed container. (a) Identify the type of the thermodynamic process (e.g, isobaric, adiabatic, isovolumetric, isothermal, or something else). Then determine the work done on the system, the amount of heat transferred to the system, and by how much the internal energy of the system has changed. (b) What is the pressure inside the container when it reaches the final temperature? R-8.31 J/(mol-K), and Helium is a monoatomic gas with mass 4 AU (atomic units) per atom and Cv 1.50 R NOTES: - If the mass of a molecule is X atomic units then the mass of one mole of the same substance is X grams - The SI unit for volume is m3 Care should be taken when applying formulas to ensure that properties with the correct units are used (if in doubt, use SI units)Explanation / Answer
As per chegg's guidlines i am answering the first one. you can ask other choices in seperate question.
(1)
Given that,
N = 10^24 molecules
W = 5 kJ
Pf = 1.75 atm
Vf = 18 L
(a)
number of moles, n = 10^24 / 6.023*10^23
n = 1.66 moles
Let final temperature = T
From ideal gas equation,
Pf*Vf = nRT
1.75*1.013*10^5 * 18*10^(-3) = 1.66*8.314*T
T = 231 K
(b)
Work done by gas,
Let initial volume = Vi
W = nRT ln (Vf / Vi)
ln (18*10^(-3) / Vi) = 5*10^3 / 1.66*8.314*231
ln (18*10^(-3) / Vi) = 1.5716
take antilog both the sides,
(18*10^(-3) / Vi) = 4.814
Vi = 3.74 L
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