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Question 1

SLPaper 1

Container X contains 1.0 mol of an ideal gas. Container Y contains 2.0 mol of the ideal gas. Y has four times the volume of X. The pressure in X is twice that in Y.

What is ${\frac{{\text{temperature of gas in X}}}{{\text{temperature of gas in Y}}}}$ ?

Question 2

SLPaper 1

A driver uses the brakes on a car to descend a hill at constant speed.

What is correct about the internal energy of the brake discs?

Question 3

SLPaper 1

A gas storage tank of fixed volume V contains N molecules of an ideal gas at temperature T. The pressure at kelvin temperature T is 20 MPa. ${\frac{N}{4}}$ molecules are removed and the temperature changed to 2T. What is the new pressure of the gas?

Question 4

SLPaper 1

The temperature of a fixed mass of an ideal gas changes from 200 °C to 400 °C.

What is $\frac{{\text{{mean kinetic energy of gas at 200 °C}}}}{{\text{{mean kinetic energy of gas at 400 °C}}}}$

Question 5

SLPaper 2

A tube of constant circular cross-section, sealed at one end, contains an ideal gas trapped by a cylinder of mercury of length 0.035 m. The whole arrangement is in the Earth’s atmosphere. The density of mercury is 1.36 × 10^4 kg m^-3.

Diagram 1

When the mercury is above the gas column the length of the gas column is 0.190 m.

The tube is slowly rotated until the gas column is above the mercury.

Diagram 2

The length of the gas column is now 0.208 m. The temperature of the trapped gas does not change during the process.

1.

A solid cylinder of height $h$ and density $\rho$ rests on a flat surface.

Show that the pressure $p_{c}$ exerted by the cylinder on the surface is given by $p_{c} = \rho gh$ .

[2]

2.

Show that $(p_o + p_m) \times 0.190 = \frac{{nRT}}{{A}}$

where $p_o$ = atmospheric pressure

$p_m$ = pressure due to the mercury column

$T$ = temperature of the trapped gas

$n$ = number of moles of the trapped gas $A$ = cross-sectional area of the tube.

[2]

3.

Determine the atmospheric pressure. Give a suitable unit for your answer.

[4]

Question 6

HLPaper 2

Titan is a moon of Saturn. The Titan-Sun distance is $9.3$ times greater than the Earth-Sun distance.

The molar mass of nitrogen is $28 \text{g} \text{mol}^{-1}$ .

1.

Show that the intensity of the solar radiation at the location of Titan is $16 W m^{-2}$ .

[1]

2.

Titan has an atmosphere of nitrogen. The albedo of the atmosphere is 0.22. The surface of Titan may be assumed to be a black body. Explain why the average intensity of solar radiation absorbed by the whole surface of Titan is $3.1 W m^{-2}$ .

[3]

3.

Show that the equilibrium surface temperature of Titan is about $90 K$ .

[1]

4.

The mass of Titan is 0.025 times the mass of the Earth and its radius is 0.404 times the radius of the Earth. The escape speed from Earth is 11.2 km/s $^{-1}$ . Show that the escape speed from Titan is 2.8 km/s $^{-1}$ .

[1]

5.

The orbital radius of Titan around Saturn is $R$ and the period of revolution is $T$ .

Show that $T^2 = \frac{4\pi^2 R^3}{GM}$ where $M$ is the mass of Saturn.

[2]

6.

The orbital radius of Titan around Saturn is $1.2 \times 10^9$ m and the orbital period is 15.9 days. Estimate the mass of Saturn.

[2]

7.

Show that the mass of a nitrogen molecule is $4.7 \times 10^{-26}$ kg.

[1]

8.

Estimate the root mean square speed of nitrogen molecules in the Titan atmosphere. Assume an atmosphere temperature of $90 K$ .

[2]

9.

Discuss, by reference to the answer in (b), whether it is likely that Titan will lose its atmosphere of nitrogen.

[1]

Question 7

SLPaper 1

Energy is supplied at a constant rate to a fixed mass of a material. The material begins as a solid. The graph shows the variation of the temperature of the material with time.

Graph

The specific heat capacities of the solid, liquid, and gaseous forms of the material are $c_s$ , $c_l$ , and $c_g$ respectively. What can be deduced about the values of $c_s$ , $c_l$ , and $c_g$ ?

Question 8

SLPaper 1

A.piece of metal at a temperature of ${100}^\circ\mathrm{C}$ is dropped into an equal mass of water at a temperature of ${15}^\circ\mathrm{C}$ in a container of negligible mass. The specific heat capacity of water is four times that of the metal.

What is the final temperature of the mixture?

Question 9

HLPaper 1

The fraction of the internal energy that is due to molecular vibration varies in the different states of matter.

What gives the order from highest fraction to lowest fraction of internal energy due to molecular vibration?

Question 10

SLPaper 1

Energy is transferred to water in a flask at a rate $P$ . The water reaches boiling point and then $P$ is increased.

What are the changes to the temperature of the water and to the rate of vaporization of the water after the change?

	Temperature	Rate of vaporization
A.	increases	unchanged
B.	increases	increases
C.	unchanged	unchanged
D.	unchanged	increases

Topic 3 - Thermal Physics

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