For one mole of an ideal gas, which of these statements must be true? (a) U and 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

JEE Main · 2020 · 04 Sep 2020 · Shift 1 · Chemical Thermodynamics

For one mole of an ideal gas, which of these statements must be true?
(a) U and H each depends only on temperature
(b) Compressibility factor Z is not equal to 1
(c)

C_{P, m} - C_{V, m} = R

(d)

dU = C_{V} dT

for any process

(A)(a), (c) and (d)✓ Correct
(B)(b), (c) and (d)
(C)(a) and (c)
(D)(c) and (d)

Answer: (A)

Solution

For an ideal gas the internal energy and enthalpy depend only on temperature, since there are no intermolecular forces, so (a) is true. The compressibility factor

Z = \frac{P V}{n R T}

equals exactly

1

for an ideal gas, so the claim in (b) that

Z \neq = 1

is false. Mayer's relation

C_{P, m} - C_{V, m} = R

holds for one mole, so (c) is true. And because

U

depends only on

T

d U = C_{V} d T

applies to any process, not just at constant volume, making (d) true. The correct statements are (a), (c) and (d).

JEE Main · 2020 · 04 Sep 2020 · Shift 1 · Single correct option

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JEE Main · 2020 · 04 Sep 2020 · Shift 1 · Chemical Thermodynamics

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