Internal energy and the ideal gas

Which statement about the internal energy of a fixed mass of an ideal gas is correct?

The temperature of a gas rises from −73 °C to 127 °C.
By what factor does the mean kinetic energy of its molecules increase?

A sealed flask of volume 2.0 × 10⁻³ m³ contains air at a pressure of 1.0 × 10⁵ Pa and a temperature of 27 °C. k = 1.38 × 10⁻²³ J K⁻¹.
How many molecules are in the flask?

A block of ice at 0 °C is heated and melts, forming water at 0 °C.
Which row describes the changes in the mean kinetic energy and in the potential energy of the molecules during the melting?

A sealed plastic bottle of air is carried in a moving car from the coast to a mountain village. The temperature of the air in the bottle stays the same throughout. Treat the air as an ideal gas.

A constant-volume gas thermometer consists of a fixed mass of gas in a rigid bulb connected to a pressure gauge. The pressure of the gas is measured at two fixed points: 0 °C: 92.0 kPa; 100 °C: 125.7 kPa. The pressure varies linearly with temperature.

Which graph shows how the mean kinetic energy of the molecules of an ideal gas varies with the Celsius temperature θ of the gas?

The graph shows the distribution of molecular speeds in two samples, X and Y, of the same gas.
Which statement is correct?

A thermometer is left inside a freezer until its reading is steady. Figure 1 shows the thermometer. Treat the air in the freezer as an ideal gas. k = 1.38 × 10⁻²³ J K⁻¹

A block of ice at −20 °C is heated by a 70 W heater. All the energy from the heater is transferred to the ice, which melts, and then to the water formed. Figure 1 shows how the temperature θ varies with time t.

A fixed mass of gas in a cylinder has a volume of 450 cm³, a pressure of 1.2 × 10⁵ Pa and a temperature of 17 °C. A piston compresses it to a volume of 180 cm³, and its temperature rises to 77 °C.
What is the new pressure of the gas?

A container holds a mixture of hydrogen molecules (mass 2.0 u) and oxygen molecules (mass 32 u) at the same temperature.
What is the ratio (r.m.s. speed of the hydrogen molecules) ÷ (r.m.s. speed of the oxygen molecules)?

The r.m.s. speed of the molecules of a gas is 480 m s⁻¹ at a temperature of 300 K.
At what temperature is the r.m.s. speed 960 m s⁻¹?

In an experiment on a fixed mass of gas at constant temperature, the volume of air trapped in a uniform tube is found from V = πd²l/4. The internal diameter is d = 1.00 ± 0.02 cm and the length of the air column is l = 25.0 ± 0.1 cm.
What is the percentage uncertainty in V?

A weather balloon is filled with helium at ground level, where the pressure is 101 kPa and the temperature is 15 °C. The volume of the balloon at ground level is 4.0 m³. k = 1.38 × 10⁻²³ J K⁻¹.

A steel cylinder of volume 5.0 × 10⁻³ m³ contains 2.4 mol of argon at 20 °C. The Avogadro constant N_A = 6.02 × 10²³ mol⁻¹. k = 1.38 × 10⁻²³ J K⁻¹. The mass of an argon atom is 40 u, where 1 u = 1.66 × 10⁻²⁷ kg.

A student investigates how the pressure of a fixed mass of air depends on its volume. The air is trapped in a gas syringe connected by a very short tube to a pressure sensor and data logger. She pushes the plunger in, in steps, and records the volume from the syringe scale and the pressure. The room temperature is 21 °C. Her results are:
V / cm³: 60, 50, 40, 30, 24, 20 — p / kPa: 101, 121, 152, 202, 252, 303.
k = 1.38 × 10⁻²³ J K⁻¹.

Air breathed out of the lungs is at body temperature, 37 °C. An oxygen molecule has a mass of 32 u, where 1 u = 1.66 × 10⁻²⁷ kg. k = 1.38 × 10⁻²³ J K⁻¹.

A sealed glass lamp contains xenon gas. When the lamp is off the xenon is at 25 °C; when it is running the xenon reaches 600 °C. The mass of a xenon atom is 131 u, where 1 u = 1.66 × 10⁻²⁷ kg. k = 1.38 × 10⁻²³ J K⁻¹.

The bar charts show the number of molecules N and the Celsius temperature θ of four samples, W, X, Y and Z, of the same ideal gas.
Which sample has the greatest internal energy?

The graph shows how the pressure p of a fixed mass of ideal gas varies with its volume V at two different constant temperatures. The lower curve is for a temperature of 300 K.
What is the temperature T of the upper curve?

A fixed mass of gas is trapped in a vertical cylinder of uniform cross-section by a piston that moves freely without friction, so the pressure of the gas stays constant. The cylinder stands in a water bath. The diagram shows the apparatus when the water is at 17 °C; the ruler measures the length of the gas column.
The water is heated to 107 °C and the gas reaches this temperature. What is the new length of the gas column?

The bar chart shows the speeds of the ten molecules in a model of a gas.
What is the root-mean-square (r.m.s.) speed of the molecules?

The graph shows how the product pV varies with the kelvin temperature T for two samples, X and Y, of an ideal gas.
What is the ratio (number of molecules in X) ÷ (number of molecules in Y)?

A gas molecule of mass 4.6 × 10⁻²⁶ kg travelling at 500 m s⁻¹ collides elastically with a flat wall, as shown in the diagram.
What is the magnitude of the change in momentum of the molecule?

Figure 1 shows how the pressure p and volume V of a fixed mass of ideal gas change as the gas is taken from state A to state B and then to state C. The temperature of the gas at A is 300 K. k = 1.38 × 10⁻²³ J K⁻¹

Figure 1 shows how the air temperature θ varies with height above sea level in the lower atmosphere. Treat the air as an ideal gas consisting of nitrogen molecules, each of mass 28 u. 1 u = 1.66 × 10⁻²⁷ kg k = 1.38 × 10⁻²³ J K⁻¹

Figure 1 shows a hand pump used to pump air into a rigid tank of volume 5.0 × 10⁻³ m³. On each stroke the pump fills with air at atmospheric pressure, 1.0 × 10⁵ Pa, and then pushes all of this air through the one-way valve into the tank. The dimensions in Figure 1 are the internal diameter of the pump barrel and the internal length swept by the piston. Assume the temperature of the air stays at 20 °C. k = 1.38 × 10⁻²³ J K⁻¹

A computer model of an ideal gas calculates the mean kinetic energy of the molecules at different kelvin temperatures. Figure 1 shows the results with a line of best fit.

Figure 1 shows apparatus used to investigate how the pressure of a fixed mass of air depends on its volume at constant temperature. Air is trapped above oil in a glass tube of uniform cross-section. A pump changes the pressure on the oil, and the Bourdon gauge shows the pressure of the trapped air.

A sealed rigid container of an ideal gas is heated from 300 K to 600 K. The pressure doubles. The average momentum change of a molecule in each collision with a wall increases by a factor of √2.
By what factor does the number of collisions per second with a wall increase?

Two flasks are joined by a thin tube, so the gas in them is at the same pressure. Flask X has a volume of 1.0 litre and is kept at 300 K. Flask Y has a volume of 2.0 litres and is kept at 450 K.
What fraction of the gas molecules is in flask Y?

A flask of volume 250 cm³ containing dry air is sealed, connected to a pressure gauge by a short narrow tube, and placed in a water bath. The water is heated and the pressure of the air is recorded at several temperatures:
θ / °C: 10, 30, 50, 70, 90 — p / kPa: 97.8, 104.7, 111.6, 118.5, 125.4.
k = 1.38 × 10⁻²³ J K⁻¹.

A gas is sealed in a rigid metal can. The can is placed in boiling water and the pressure of the gas increases.

The kinetic theory of gases models a gas as N molecules, each of mass m, moving at random in a cube of side L.

A student traps a fixed mass of air at 17 °C and measures its pressure p at different volumes V, keeping the temperature constant. The graph shows p against 1/V, with a line of best fit through the origin. P is a point on the line. k = 1.38 × 10⁻²³ J K⁻¹
How many air molecules are trapped?

The graph shows how the mean square speed ⟨c²⟩ of the molecules of a gas varies with the kelvin temperature T. P is a point on the line. k = 1.38 × 10⁻²³ J K⁻¹ 1 u = 1.66 × 10⁻²⁷ kg
What is the mass of one molecule of the gas?

A student investigates how the pressure p of a fixed mass of air depends on its volume V at a constant temperature of 25 °C. She plots lg (p / kPa) against lg (V / cm³), as shown in Figure 1, and draws a line of best fit. k = 1.38 × 10⁻²³ J K⁻¹

A sealed metal can of volume 4.0 × 10⁻⁴ m³ contains a gas. The can is heated slowly and the pressure p of the gas is recorded at different kelvin temperatures T. At 400 K a safety valve opens briefly, lets some gas escape and closes again. Figure 1 shows the results. The volume of the can does not change. k = 1.38 × 10⁻²³ J K⁻¹

Figure 1 shows a gas in a cylinder of uniform cross-section fitted with a pressure gauge, before and after the piston is pushed in slowly. The temperature of the gas stays at 20 °C throughout and no gas escapes. Treat the gas as ideal.