CAIE A-Level Physics 15.2 Equation of State

Practise distinguishing ideal-gas behaviour and applying pV = nRT or pV = NkT with consistent units, mole data or molecule data.

Exam points

identify ideal-gas behaviour and apply pV = nRT or pV = NkT to calculate state variables
use k = R/N_A and choose the appropriate mole or molecule form of the equation of state

Covered syllabus points

15.2.1—A gas obeying pV ∝ T, where T is the thermodynamic temperature, is known 15.2.2—The equation of state for an ideal gas expressed as pV = nRT 15.2.3—That the Boltzmann constant k is given by k = R / NA

[Maximum number: 5]

(a)

State what is meant by an ideal gas.

[ 2 ]

(gas that obeys) $p V \propto T$ (for all values of p, V and T )

M1

where T is thermodynamic temperature

A1

(b)

A sealed vessel contains a mass of 0.0424 kg of an ideal gas at $227^{\circ} \mathrm{C}$ . The pressure of the gas is $1.37 \times 10^{5} \mathrm{~Pa}$ and the volume of the gas is $0.640 \mathrm{~m}^{3}$ .

Calculate:

[ 3 ]

(i)

the number of molecules of the gas in the vessel

[ 3 ]

p V=N k T

C1

$N=\left(1.37 \times 10^{5} \times 0.640\right) /\left(1.38 \times 10^{-23} \times(227+273)\right)$

C1

$=1.27 \times 10^{25}$

A1

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Covered syllabus points

15.2 Equation of state question 1

Question (a)

Question (b)

Question (i)