DP Physics (last assessment 2024)

Question 23M.3.HL.TZ2.19

19.

[Maximum mark: 4]

23M.3.HL.TZ2.19

(a)

State the Jeans criterion for the collapse of interstellar clouds.

[1]

Markscheme

M > M_j

minimum mass for interstellar matter to collapse into a star

«interstellar» potential energy > kinetic energy ✓

Do not penalize if they compare gravitational force with kinetic, thermal or internal energy.

(b)

For a main sequence star, the energy it releases during the total time T it spends on the main sequence is proportional to its mass M.

(b.i)

Show that T ∝ $\frac{1}{M^{2.5}}$ .

[2]

Markscheme

ALTERNATIVE 1

T ∝ $\frac{M}{L}$ L ∝ $\frac{M}{T}$ ✓

«and L proportional to M^3.5 then»

T ∝ $\frac{M}{M^{3.5}}$ ✓

ALTERNATIVE 2

L proportional $\frac{E}{T}$ ✓

AND

L proportional M ✓

«and L proportional to M^3.5 then»

T proportional $\frac{M}{M^{3.5}}$ ✓

MP2 can be awarded if MP1 is not.

(b.ii)

For the Sun, T = 10¹⁰ years. Calculate T for a star 20 times more massive than the Sun.

[1]

Markscheme

« $T_{20} M_{20}^{2.5} = T_{sun} M_{sun}^{2.5}$ OR $T_{20} = 10^{10} \times {(\frac{1}{20})}^{2.5}$ »

«T₂₀ = » 1.8 × 10⁹ «s» OR 5.6 × 10⁶ «y» ✓

Accept 5.6 My if unit stated