Question:
For one mole of an ideal gas, which of these statements must be true ?
(a) $\mathrm{U}$ and $\mathrm{H}$ each depends only on temperature
(b) Compressibility factor $\mathrm{z}$ is not equal to 1
(c) $\mathrm{C}_{\mathrm{P}, \mathrm{m}}-\mathrm{C}_{\mathrm{V}, \mathrm{m}}=\mathrm{R}$
(d) $\mathrm{dU}=\mathrm{C}_{\mathrm{V}} \mathrm{dT}$ for any process
Correct Option: 1
Solution:
For ideal Gas
$\# \mathrm{U}=\mathrm{f}(\mathrm{T}), \mathrm{H}=\mathrm{f}(\mathrm{T})$
$\# \mathrm{Z}=1$
$\# \mathrm{C}_{\mathrm{P}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R}$
$\# \mathrm{dU}=\mathrm{C}_{\mathrm{V}} \mathrm{dT}$
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