Physics 9702 · AS & A Level · Kinetic theory of gases

Kinetic theory of gases — practice question

A gas begins at a temperature of $27.2^\circ\text{C}$ and is then heated until it reaches $38.8^\circ\text{C}$. Calculate, in kelvin, to a suitable number of decimal places,
(a(i))[2]

the gas’s starting temperature.

(a(ii))[1]

the temperature rise.

(b(i))[1]

State what the symbol $\langle c^2 \rangle$ means in the expression $p = \frac{1}{3} \rho \langle c^2 \rangle$.

(b(ii))[4]

Use the expression $p = \frac{1}{3} \rho \langle c^2 \rangle$ to show that the mean kinetic energy $\langle E_K \rangle$ of the atoms in an ideal gas is $\langle E_K \rangle = \frac{3}{2} kT$. Explain any symbols that you use.

(c(i))[2]

Calculate how much gas there is.

(c(ii))[2]

Calculate the atoms’ mean kinetic energy.

(c(iii))[3]

Calculate the gas’s total internal energy.

Worked solution & mark scheme

This 15-mark question has a full step-by-step worked solution and mark scheme. One marking point: Express in kelvin: $27.2 + 273.15$ or $27.2 + 273.2$

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI