Chapter 4 Second Law of Ther modynamics 1 A Carnot engine o

Chapter 4 - Second Law of Ther modynamics 1.) A Carnot engine operates between 500 K and 300 K. The engine contains 100 moles of ideal gas as the working material. The initial volume of the gas before expansion of stroke 1 is 410.3L After the first expansion stroke, the volume is 1641.2 L a.) How much work is done per cycle for this engine? b.) If the gas is monatomic, what is the volume of the gas after the adiabatic stroke 2 is completed? c.) What is the volume of the gas after the completion of stroke 3?

Solution

a)

W_tot= -nRT₁ln(V₂/V₁) -nRT₂ln(V₁/V₂)

=-nR ln(V₂/V₁)(T₁-T₂)

Substitute the values.

W_tot=-(100moles)(8.314 J mol^-1 K^-1)ln(1641.3L / 410.3L) (500K - 300K)

=230523.15 J

=2.30X10⁵J

b)

For monatomic gas, the molar heat capacity at constant volume is C_v=1.5R

The ratios of V_2,V₃and T_2,T₁are related as,

V₂/V₃=(T₂/T₁)^C_v/R

V₃=V₂(T₁/T₂)^C_v/R

=1641.2L (500K/300K) ^1.5

=3531.3L

C)

The ratios of volume can be written as,

V₂/V₃=V₁/V₄

V₄=(V₁V₃)/V₂

=(410.3L * 3531.3L)/ 1641.2L

=882.8L