[3] a) Calculate the efficiency for a Carnot engine operating between 800K and 2

Question

[3] a) Calculate the efficiency for a Carnot engine operating between 800K and 250K. Suppose that, instead of an adiabatic expansion for doing work, an engine used constant pressure expansion between the same temperatures for doing work. Use n=0.1 mol, V1=6.0L, T1=800K and heat = 3kJ

b) Use the isothermal heat relation to calculate the volume after heat absorption.

c) Calculate the pressure at the new volume.

d) The gas expands at constant pressure, dropping the temperature to 250K. Calculate the new volume after expansion.

e) Calculate the PV work done during the constant pressure expansion.

f) Calculate the efficiency of such an engine. Remember the efficiency = work out over heat in.

Explanation / Answer

a)then the efficiency of carnot's engine is ( 1 - T2 /T1 ) x100

=(1-250/800)*100

=68.75%

b)delta U

Because it is isothermal, there is no change of temperature, it means that deltaU is zero

Q= deltaU + W

Q=W

W= n*R*T* ln (V1/V2)

3000=0.1*8.314*800ln(6/V2)

4.5=ln(6/V2)

4.5=1.79/ln(V2)

0.39=ln(V2)

V2=2.45L

c)Pv=nRt

P=nRT/V

=0.1*8.314*800/2.5

=266

d)V2 = V1T2 / T1

V2=6*250/800

=1.8L

e)The work done by the gas is p delta-V

Work = n R ?T

=0.1*8.314*(800-250)

=457.27J

f)efficiency = work out over heat in.

=57.27J/0

=0

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