d)

i) To calculate the root mean square speed of the gas molecules:

List the known quantities (remembering to convert degrees Celsius to kelvin):

From the data booklet:

Recall the equation relating root mean square speed, mass and temperature:

Rearrange to make ${c_{r m s}}^{2}$ the subject:

Substitute the values and calculate:

${c_{r m s}}^{2} = \frac{3 \times (1.38 \times 10^{- 23}) \times 523}{(4.8 \times 10^{- 26})} = 451 088$ [1 mark]

Take the square root:

Round the answer to two significant figures and include the units:

ii) To calculate internal energy:

List the known quantities:

From the data booklet:

Determine the number of molecules:

Number of molecules, $N = n \times N_{A} = 1.3 \times (6.02 \times 10^{23}) = 7.826 \times 10^{23}$ [1 mark]

Substitute the know quantities into the equation for the mean kinetic energy of molecules in a gas and calculate:

$E = \frac{3}{2} \times (1.38 \times 10^{- 23}) \times 523 = 1.08 \times 10^{- 20}$ [1 mark]

Multiply the average kinetic energy per molecule by the total number of molecules to find the total internal energy:

$K E_{t o t a l} = N \times E$
$K E_{t o t a l} = (7.826 \times 10^{23}) \times (1.08 \times 10^{- 20}) = 8452$

Round the answer to two significant figures and include the units:

[Total: 6 marks]

Region	Physical quantity, or quantities, that increases as time increases	Physical quantity, or quantities, that remain constant as time increases
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Fig. 17.1	Fig. 17.2

Thermal Properties of Materials (OCR A Level Physics)

Exam Questions