MCQ
Select the incorrect relation. (Where symbols have their usual meanings)
- A${C_P} = \frac{{\gamma R}}{{\gamma - 1}}$
- B${C_P} - {C_V} = R$
- ✓$\Delta U = \frac{{{P_f}{V_f} - {P_i}{V_i}}}{{1 - \gamma }}$
- D${C_V} = \frac{R}{{\gamma - 1}}$
✓
Answer
Correct option: C.
$\Delta U = \frac{{{P_f}{V_f} - {P_i}{V_i}}}{{1 - \gamma }}$
c
$\Delta \mathrm{U}=\mu \mathrm{C}_{\mathrm{V}} \Delta \mathrm{T}=\mu \mathrm{C}_{\mathrm{V}}\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right)=\frac{\mu \mathrm{R}}{\gamma-1}\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right)$
$\Delta \mathrm{U}=\mu \mathrm{C}_{\mathrm{V}} \Delta \mathrm{T}=\mu \mathrm{C}_{\mathrm{V}}\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right)=\frac{\mu \mathrm{R}}{\gamma-1}\left(\mathrm{T}_{2}-\mathrm{T}_{1}\right)$
$=\frac{\mu \mathrm{RT}_{2}-\mu \mathrm{RT}_{1}}{\gamma-1}=\frac{\mathrm{P}_{\mathrm{f}} \mathrm{V}_{\mathrm{f}}-\mathrm{P}_{\mathrm{i}} \mathrm{V}_{\mathrm{i}}}{\gamma-1}$
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