# 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 $z$ 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. (1) (a) and (c)

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

3.  (c) and (d)

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

Correct Option: , 4

Solution:

(a) For ideal gas $\mathrm{U}$ and $\mathrm{H}$ are function of temperature.

(b) Compressibility factor for an ideal gas is $1 .$

(c) $\mathrm{C}_{\mathrm{P}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R}$

(d) $\Delta \mathrm{U}=\mathrm{CvdT}$ for all processes.