Question

1- A heat engine operates between two reservoirs at temperatures of 70◦C and 170◦C. What is the maximum efficiency possible for this engine?

2)The molecular mass of helium is 4 g/mol, the value of Boltzmann’s constant is 1.38066 × 10−23 J/K, the universal gas constant is 8.31451 J/K · mol, and Avogadro’s number is 6.02214 × 1023 1/mol. How many atoms of helium gas are required to fill a balloon to diameter 35 cm at 17◦C and 1.787 atm? 1 atm = 101300 Pa.

Answer 1

1. efficiency of heat engine is 1- T1/T2

T1 = 70 +273 = = 343 k

T2 = 170 +273 = 443 K

e = 1 - 343/443

e = 22.5 %

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2. use ideal gas eqaution

PV = nRT

here V is Volume =4/3 pi r^3

r = D/2 = 0.35/2 = 0.175 m

so

V = (4/3) * 3.14 * 0.175^3

V = 0.0224 m^3

so

n = PV/RT

n = (1.78 * 101300 * 0.0224)/(8.314 * (17+273))

n= 1.675 moles

No. of atoms N = n * Avagodro no.s

N = 1.675 * 6.02214*10^23

N = 1 *10^24 atoms

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