B.3 Gas laws

Practice Worksheet — name: ______________________ date: ____________

Formulas for this topic

Pressure

P = \frac{F}{A}

Amount of substance

n = \frac{N}{N_{A}}

Ideal gas law

PV = nRT = Nk_{B}T

Combined gas law

\frac{P_{1}V_{1}}{T_{1}} = \frac{P_{2}V_{2}}{T_{2}}

Pressure (kinetic theory)

P = \tfrac{1}{3}\rho v^{2}

Internal energy (monatomic)

U = \tfrac{3}{2}Nk_{B}T = \tfrac{3}{2}nRT

Section A — Multiple choice

A1. A fixed mass of ideal gas is heated at constant volume. Its pressure rises because the molecules:

A Expand and take up more space
B Collide with the walls more often and with greater momentum change
C Repel each other more strongly
D Increase in mass

A2. An ideal gas at 27 °C is heated at constant pressure until its volume doubles. Its new temperature is:

A 54 °C
B 600 K
C 327 °C
D 150 K

A3. A real gas behaves most like an ideal gas at:

A High pressure and low temperature
B High pressure and high temperature
C Low pressure and high temperature
D Low pressure and low temperature

Section B — Short answer

B1. A diver's air bubble has volume $2.0\ \text{cm}^3$ at a depth where the pressure is 3.0 atm and the temperature 280 K. Find its volume just below the surface, at 1.0 atm and 300 K. [3 marks]

B2. State three assumptions of the kinetic model of an ideal gas. [3 marks]

B3. Calculate the internal energy of 2.0 mol of an ideal monatomic gas at 300 K, and state why this equals its total kinetic energy. [3 marks]

Answer key

For worked explanations, interactive practice and more free resources, visit www.newtonine.com

Section A

A1: Collide with the walls more often and with greater momentum change — Higher temperature means higher average speed: each wall collision transfers more momentum, and collisions come more frequently. Both effects raise the rate of momentum transfer per unit area — which is what pressure is.

A2: 600 K — Charles's law needs kelvin: $T_1 = 300\ \text{K}$ ; doubling $V$ at constant $P$ doubles $T$ , giving 600 K (327 °C — note that "54 °C" is the trap for students who double the Celsius value).

A3: Low pressure and high temperature — Ideality requires molecular volume to be negligible compared with the container (low pressure/density) and kinetic energy to swamp intermolecular attractions (high temperature). Near condensation, both assumptions fail.

Section B

B1: $\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$ : $V_2 = 2.0 \times \frac{3.0}{1.0} \times \frac{300}{280} \approx 6.4\ \text{cm}^3$ . The pressure drop dominates; the temperature rise adds a small extra expansion.

B2: Any three of: molecules are point particles whose total volume is negligible compared with the gas volume; no intermolecular forces act except during collisions; collisions are perfectly elastic; molecules move randomly; the duration of collisions is negligible compared with the time between them.

B3: $U = \frac{3}{2}nRT = \frac{3}{2}(2.0)(8.31)(300) \approx 7.5\ \text{kJ}$ . For an ideal gas there are no intermolecular forces, hence no molecular potential energy — internal energy is purely the random translational kinetic energy of the molecules.