For one mole of an ideal gas,
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

1. (a), (c) and (d)

2. (b), (c) and (d)

3. (c) and (d)

4. (a) and (c)

Correct Option: 1

Solution:

For ideal Gas

$\# \mathrm{U}=\mathrm{f}(\mathrm{T}), \mathrm{H}=\mathrm{f}(\mathrm{T})$

$\# \mathrm{Z}=1$

$\# \mathrm{C}_{\mathrm{P}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R}$

$\# \mathrm{dU}=\mathrm{C}_{\mathrm{V}} \mathrm{dT}$