PRELIMINARY STAGE 2024
Contest 1
Mfantsiman Girls’ SHS: 44 points (Winner)
West Africa SHS: 41 points
Zion College: 37 points
Contest 2
Simms SHS: 43 points (Winner)
Hope College: 37 points
Kpando SHS: 36 points
Contest 3
Archbishop Porter Girls’ SHS: 45 points (Winner)
Wenchi Methodist SHS: 39 points
Ejisuman SHS: 37 points
ROUND 4 - TRUE OR FALSE
1. The heat capacity of an ideal gas depends on how the gas is heated.
ANSWER: TRUE
EXPLANATION:
For an ideal gas, the heat capacity changes depending on the heating process.
When the gas is heated at constant volume, its heat capacity is called CV.
When the gas is heated at constant pressure, its heat capacity is called CP.
These two values are different because at constant pressure the gas also expands.
So the heat capacity depends on how the gas is heated.
2. If an ideal gas is heated at constant volume, all the heat supplied increases the internal energy of the gas.
ANSWER: TRUE
EXPLANATION:
At constant volume, the gas cannot expand, so it does no external work.
Because no work is done, all the heat supplied goes into increasing the internal energy and raising the temperature of the gas.
3. If an ideal gas is heated at constant pressure, all the heat supplied increases the internal energy of the gas.
ANSWER: FALSE
EXPLANATION:
At constant pressure, the gas expands when heated.
This means the heat supplied does two things:
Increases the internal energy.
Does work as the gas expands.
Therefore, not all the heat goes into internal energy.
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PRACTICE QUESTIONS
1. QUESTION: The molar heat capacity of an ideal gas at constant pressure is greater than at constant volume.
ANSWER: TRUE
EXPLANATION:
At constant pressure some heat is also used to do work as the gas expands.
2. QUESTION: For an ideal gas, $C_p - C_v = R$ per mole.
ANSWER: TRUE
EXPLANATION:
This is Mayer's relation.
3. QUESTION: An ideal gas heated at constant volume does work on its surroundings.
ANSWER: FALSE
EXPLANATION:
Its volume does not change, so it does no work.
4. QUESTION: The ratio $\dfrac{C_p}{C_v}$ is less than 1 for every ideal gas.
ANSWER: FALSE
EXPLANATION:
$C_p$ is greater than $C_v$, so the ratio is greater than 1.
5. QUESTION: For a monatomic ideal gas, $C_v = \dfrac{3}{2}R$ per mole.
ANSWER: TRUE
EXPLANATION:
It has three translational degrees of freedom, each giving $\dfrac{1}{2}R$.
6. QUESTION: For a monatomic ideal gas, $\gamma = \dfrac{5}{3}$.
ANSWER: TRUE
EXPLANATION:
$C_p = \dfrac{5}{2}R$ and $C_v = \dfrac{3}{2}R$.
7. QUESTION: An ideal gas has only one value of heat capacity.
ANSWER: FALSE
EXPLANATION:
It depends on the process, for example constant volume or constant pressure.
8. QUESTION: When an ideal gas is heated at constant pressure, its internal energy does not change.
ANSWER: FALSE
EXPLANATION:
Its temperature rises, so its internal energy increases.
9. QUESTION: An ideal gas heated at constant pressure expands.
ANSWER: TRUE
EXPLANATION:
At constant pressure $V \propto T$.