[Maximum number: 3]

A cylinder contains 5.12 mol of an ideal gas at pressure $5.60 \times 10^{5} \mathrm{~Pa}$ and volume $3.80 \times 10^{-2} \mathrm{~m}^{3}$ .

(a)

Calculate the thermodynamic temperature of the gas.

temperature =

[ 2 ]

(b)

The average kinetic energy $E_{\mathrm{K}}$ of a molecule of the gas is given by the expression

E_{\mathrm{K}}=\frac{3}{2} k T

where k is the Boltzmann constant and T is the thermodynamic temperature.
The gas is heated at constant pressure so that its temperature rises by 125 K .

[ 1 ]

(i)

Show that the new volume of the gas is $4.75 \times 10^{-2} \mathrm{~m}^{3}$ .

[ 1 ]

[Maximum number: 2]

+w.

(a)

Argon-40 $\left({ }_{18}^{40} \mathrm{Ar}\right)$ may be assumed to be an ideal gas.

A mass of 3.2 g of argon- 40 has a volume of $210 \mathrm{~cm}^{3}$ at a temperature of $37^{\circ} \mathrm{C}$ .
Determine, for this mass of argon-40 gas,

[ 2 ]

(i)

the pressure,
pressure = Pa

[ 2 ]

[Maximum number: 1]

the rise in temperature of the gas.
temperature rise = K

(a)

The volume of an ideal gas in a cylinder is $1.80 \times 10^{-3} \mathrm{~m}^{3}$ at a pressure of $2.60 \times 10^{5} \mathrm{~Pa}$ and a temperature of 297 K , as illustrated in Fig. 2.1.

Fig. 2.1

The thermal energy required to raise the temperature by 1.00 K of 1.00 mol of the gas at constant volume is 12.5 J .

The gas is heated at constant volume such that the internal energy of the gas increases by 95.0 J .

[ 1 ]

(i)

Calculate

(ii)

Use your answer in (i) part 2 to show that the final pressure of the gas in the cylinder is $2.95 \times 10^{5} \mathrm{~Pa}$ .

[ 1 ]

[Maximum number: 2]

the rate h of thermal energy gained by the ice from the surroundings.

h=

W

(a)

The variation with volume V of the pressure p of an ideal gas as it undergoes a cycle ABCA of changes is shown in Fig. 2.1.

Fig. 2.1

The temperature of the gas at A is 290 K . The temperature at B is 870 K .

Determine

(i)

the temperature of the gas at C .
temperature = K

(a)

Two containers A and B are joined by a tube of negligible volume, as illustrated in Fig. 2.1.

Fig. 2.1

The containers are filled with an ideal gas at a pressure of $2.3 \times 10^{5} \mathrm{~Pa}$ .
The gas in container A has volume $3.1 \times 10^{3} \mathrm{~cm}^{3}$ and is at a temperature of $17^{\circ} \mathrm{C}$ .
The gas in container B has volume $4.6 \times 10^{3} \mathrm{~cm}^{3}$ and is at a temperature of $30^{\circ} \mathrm{C}$ .
Calculate the total amount of gas, in mol, in the containers.
amount = mol

[ 4 ]

[Maximum number: 2]

A constant mass of an ideal gas has a volume of $3.49 \times 10^{3} \mathrm{~cm}^{3}$ at a temperature of $21.0^{\circ} \mathrm{C}$ . When the gas is heated, 565 J of thermal energy causes it to expand to a volume of $3.87 \times 10^{3} \mathrm{~cm}^{3}$ at $53.0^{\circ} \mathrm{C}$ . This is illustrated in Fig.2.1.

Fig. 2.1

(a)

Show that the initial and final pressures of the gas are equal.

[ 2 ]

[Maximum number: 1]

Fig. 2.1 shows a laboratory thermometer that is calibrated to measure temperature in degrees Celsius.

Fig. 2.1

The thermometer makes use of the fact that the density of mercury varies with temperature.

(a)

(i)

Thermodynamic temperature T may be determined by the behaviour of a type of substance for which T is proportional to the product of pressure and volume.

State the name of this type of substance.

[ 1 ]

[Maximum number: 1]

The product of the pressure p and the volume V of an ideal gas is given by the expression

p V=\frac{1}{3} N m<c^{2}>

where m is the mass of one molecule of the gas.

(a)

State the meaning of the symbol

[ 1 ]

(i)

N,

[ 1 ]

(a)

A fixed mass of an ideal gas at a temperature of $20^{\circ} \mathrm{C}$ is sealed in a cylinder by a piston, as shown in Fig. 2.1.

Fig. 2.1

The initial volume of the gas is $1.24 \times 10^{-4} \mathrm{~m}^{3}$ .
Thermal energy is supplied to the gas and its volume increases by $5.20 \times 10^{-5} \mathrm{~m}^{3}$ .

[ 2 ]

(i)

Calculate the final thermodynamic temperature T of the gas.

T=

[ 2 ]

(a)

A balloon is filled with helium gas at a pressure of $1.1 \times 10^{5} \mathrm{~Pa}$ and a temperature of $25^{\circ} \mathrm{C}$ .
The balloon has a volume of $6.5 \times 10^{4} \mathrm{~cm}^{3}$ .
Helium may be assumed to be an ideal gas.
Determine the number of gas atoms in the balloon.
number =

[ 4 ]

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