(a)

(i)

State what is meant by the internal energy of a system.

[ 2 ]

[Maximum number: 2]

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

h=

W

(a)

State what is meant by internal energy.

[ 2 ]

[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)

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 .

[ 3 ]

(i)

Calculate the increase in internal energy of the gas. Explain your working.

[ 3 ]

[Maximum number: 4]

the period of Deimos in its orbit about Mars.
period = hours

(a)

(i)

State what is meant by the internal energy of a substance.

[ 2 ]

(ii)

Use the equation in (b)(ii) to explain that, for an ideal gas, a change in internal energy $\Delta U$ is given by

\Delta U \propto \Delta T

where $\Delta T$ is the change in temperature of the gas.

[ 2 ]

[Maximum number: 3]

electric potential energy.
energy = J

(a)

Helium-4 may be assumed to behave as an ideal gas.

A cylinder has a constant volume of $7.8 \times 10^{3} \mathrm{~cm}^{3}$ and contains helium-4 gas at a pressure of $2.1 \times 10^{7} \mathrm{~Pa}$ and at a temperature of 290 K .

Calculate, for the helium gas,

[ 3 ]

(i)

the total internal energy.
internal energy = J

[ 3 ]

[Maximum number: 3]

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)

Explain why the change in kinetic energy of the molecules of this ideal gas is equal to the change in internal energy.

[ 3 ]

[Maximum number: 4]

A student suggests that, when an ideal gas is heated from $100^{\circ} \mathrm{C}$ to $200^{\circ} \mathrm{C}$ , the internal energy of the gas is doubled.

(a)

(i)

State what is meant by internal energy.

[ 2 ]

(b)

State and explain whether the student's suggestion is correct.

[ 2 ]

(a)

A negative temperature coefficient thermistor may be used as a type of resistance thermometer.

State one way in which the variation with temperature of the resistance of a thermistor differs from that of a platinum wire.

[ 1 ]

(a)

By referring to both kinetic energy and potential energy, explain what is meant by the internal energy of an ideal gas.

[ 2 ]

[Maximum number: 4]

air and soft tissue.

\alpha=

(a)

(i)

State what is meant by the internal energy of a substance.

[ 2 ]

(ii)

Explain why an increase in internal energy of an ideal gas is directly related to a rise in temperature of the gas.

[ 2 ]