First slide

Thermodynamic processes

Question

Carbon monoxide is carried around a closed cycle abc in which bc is an isothermal process as shown in the figure. The gas absorbs 7000J of heat as its temperature 300k to 1000k in going from a to b. The quantity of heat rejected by the gas during the process ca is

Difficult

A

4200J
B

5000J
C

9000J
D

9800J

Solution

For path $a b : {(Δ U)}_{a b} = 7000 J$
By using $Δ U = n C_{v} Δ T$
$7000 = n \times \frac{5}{2} R \times 700$
n = 0.48
For path $c a : {(Δ Q)}_{c a} = {(Δ U)}_{c a} + {(Δ W)}_{c a} - - - - (1)$
$\begin{array}{l} ∵ (ΔU)_{a b} + (Δ U)_{b c} + (Δ U)_{c a} = 0 \\ ∴ 7000 + 0 + (ΔU)_{c a} = 0 \\ (Δ U)_{c a} = - 7000 J - - - - (2) \end{array}$
Also ${(Δ W)}_{c a} = P_{1} (V_{1} - V_{2}) = n R (T_{1} - T_{2})$
= -2792.16 J--------(3)
Solving (1), (2) and (3)
${(Δ Q)}_{c a} = - 7000 - 2792.16$
=-9792.16J
=-9800J

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