EduNinja
[Maximum number: 2]

+w.

(a)

Argon-40 (1840Ar)\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 cm3210 \mathrm{~cm}^{3} at a temperature of 37∘C37^{\circ} \mathrm{C}.
Determine, for this mass of argon-40 gas,

[ 2 ]
(i)

the pressure,
pressure = Pa

[ 2 ]
(a)

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

Fig. 2.1

Fig. 2.1

The containers are filled with an ideal gas at a pressure of 2.3×105 Pa2.3 \times 10^{5} \mathrm{~Pa}.
The gas in container A has volume 3.1×103 cm33.1 \times 10^{3} \mathrm{~cm}^{3} and is at a temperature of 17∘C17^{\circ} \mathrm{C}.
The gas in container B has volume 4.6×103 cm34.6 \times 10^{3} \mathrm{~cm}^{3} and is at a temperature of 30∘C30^{\circ} \mathrm{C}.
Calculate the total amount of gas, in mol, in the containers.
amount = mol

[ 4 ]
[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

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

[Maximum number: 1]

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

(a)

The volume of an ideal gas in a cylinder is 1.80×10−3 m31.80 \times 10^{-3} \mathrm{~m}^{3} at a pressure of 2.60×105 Pa2.60 \times 10^{5} \mathrm{~Pa} and a temperature of 297 K , as illustrated in Fig. 2.1.

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 2.95×105 Pa2.95 \times 10^{5} \mathrm{~Pa}.

[ 1 ]
[Maximum number: 3]

A cylinder contains 5.12 mol of an ideal gas at pressure 5.60×105 Pa5.60 \times 10^{5} \mathrm{~Pa} and volume 3.80×10−2 m33.80 \times 10^{-2} \mathrm{~m}^{3}.

(a)

Calculate the thermodynamic temperature of the gas.

temperature =
[ 2 ]
(b)

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

EK=32kTE_{\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 4.75×10−2 m34.75 \times 10^{-2} \mathrm{~m}^{3}.

[ 1 ]
[Maximum number: 2]

A constant mass of an ideal gas has a volume of 3.49×103 cm33.49 \times 10^{3} \mathrm{~cm}^{3} at a temperature of 21.0∘C21.0^{\circ} \mathrm{C}. When the gas is heated, 565 J of thermal energy causes it to expand to a volume of 3.87×103 cm33.87 \times 10^{3} \mathrm{~cm}^{3} at 53.0∘C53.0^{\circ} \mathrm{C}. This is illustrated in Fig.2.1.

Fig. 2.1

Fig. 2.1

(a)

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

[ 2 ]
(a)

A fixed mass of an ideal gas at a temperature of 20∘C20^{\circ} \mathrm{C} is sealed in a cylinder by a piston, as shown in Fig. 2.1.

Fig. 2.1

Fig. 2.1

The initial volume of the gas is 1.24×10−4 m31.24 \times 10^{-4} \mathrm{~m}^{3}.
Thermal energy is supplied to the gas and its volume increases by 5.20×10−5 m35.20 \times 10^{-5} \mathrm{~m}^{3}.

[ 2 ]
(i)

Calculate the final thermodynamic temperature T of the gas.

T=
[ 2 ]
[Maximum number: 1]

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

Fig. 2.1

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

pV=13Nm<c2>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 balloon is filled with helium gas at a pressure of 1.1×105 Pa1.1 \times 10^{5} \mathrm{~Pa} and a temperature of 25∘C25^{\circ} \mathrm{C}.
The balloon has a volume of 6.5×104 cm36.5 \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 ]
0