, and temperature of 300K. Assume that the oxygen acts as an ideal gas. The foll

Question

, and temperature of 300K. Assume that the oxygen acts as an ideal gas. The following process is carried out on the gas:
i. Isobaric heating from its initial state to state 2 with T=450 K.
ii. Cooled to state 3 isochorically to 250K.
iii. Compressed isothermally to state 4 where the volume is 4.00 liters.
iv. Heated isochorically to 300K back to state 1.
Draw a P-V diagram for the four states giving the values of P and V for each state. Calculate q and w for each of the four processes. What is the efficiency of this device as a heat engine? How does this engine compare with a Carnot engine operating between the same minimum and maximum temperatures?

Explanation / Answer

P V = n R T    the number of moles of oxygen canwritten as    n = P1 V1 / RT1    the heat capacities are taken from the table inthe chapters so that we get    P1 V1 = 810.40J             = x (assume)    so in the first process we get the value ofQ as (i)    Q = n Cp T        = (Cp /R) (x) [(T2 / T1) - 1]        = (3.508) (810.4 J) (1 /2)        = 1421.4 J (ii)    Q = n CV T        = (CV /R) (x) [(T3 - T2) /T1]        = (2.508) (810.4 J) (- 2/ 3)        = -1354.98 J (iii)    in this process the energy is same as that of theworkdone given by    Q = W        = n R T3ln(V4 / V3)        = (x) (T3 /T1) ln (V4 / V3)        = (810.4 J) (5 / 6)ln (2 / 3)        = -273.82 J (iv)    Q = n CV T        = (CV /R) (x) [1 - (T4 / T1)]        = (2.508) (810.4 J) (1 /6)        = 338.74 J        = (CV /R) (x) [(T3 - T2) /T1]        = (2.508) (810.4 J) (- 2/ 3)        = -1354.98 J (iii)    in this process the energy is same as that of theworkdone given by    Q = W        = n R T3ln(V4 / V3)        = (x) (T3 /T1) ln (V4 / V3)        = (810.4 J) (5 / 6)ln (2 / 3)        = -273.82 J (iv)    Q = n CV T        = (CV /R) (x) [1 - (T4 / T1)]        = (2.508) (810.4 J) (1 /6)        = 338.74 J        = (CV /R) (x) [1 - (T4 / T1)]        = (2.508) (810.4 J) (1 /6)        = 338.74 J

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