22. a student measures the same gas sample at different conditions. at which condition would the gas have the highest density?
mark only one oval.
high temperature, high pressure
high temperature, low pressure
low temperature, high pressure
low temperature, low pressure
23. during an adiabatic expansion of a gas, which statement is most accurate? * 1 point
mark only one oval.
pressure increases to maintain constant internal energy
temperature remains constant because no heat is exchanged
temperature increases because volume increases
temperature decreases because the gas does work on surroundings
24. why does it require more energy to convert water at 100°c to steam at 100°c than to heat water from 0°c to 100°c? * 1 point
mark only one oval.
the latent heat of vaporization is greater than the sensible heat required
pressure changes require additional energy
steam has higher specific heat than liquid water
steam molecules have more kinetic energy

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# Brief Explanations:
- **Question 22**:
    - Density of a gas is given by $
ho=\frac{m}{V}$.
    - From the ideal gas law $PV = nRT$, we can express $V=\frac{nRT}{P}$. So $
ho=\frac{mP}{nRT}$.
    - Since $m$ and $n$ (for a given gas sample) are constant, $
ho\propto\frac{P}{T}$.
    - A low temperature ($T$) and high pressure ($P$) will give the highest value of $\frac{P}{T}$, thus the highest density.
- **Question 23**:
    - In an adiabatic process $Q = 0$.
    - The first law of thermodynamics is $\Delta U=Q - W$. Since $Q = 0$, $\Delta U=-W$.
    - When a gas expands adiabatically, it does work on the surroundings ($W>0$), so $\Delta U<0$.
    - Internal energy $U$ is a function of temperature ($U = nC_{v}T$ for an ideal gas). A decrease in $U$ means a decrease in $T$.
- **Question 24**:
    - When heating water from $0^{\circ}C$ to $100^{\circ}C$, we are providing sensible heat ($Q = mc\Delta T$).
    - When converting water at $100^{\circ}C$ to steam at $100^{\circ}C$, we are providing latent heat of vaporization ($Q = mL_{v}$).
    - The latent heat of vaporization ($L_{v}$) for water is much larger than the product of specific heat ($c$) and temperature change ($\Delta T = 100^{\circ}C$) for the same mass of water.

# Answer:
- **Question 22**: Low temperature, high pressure
- **Question 23**: Temperature decreases because the gas does work on surroundings
- **Question 24**: The latent heat of vaporization is greater than the sensible heat required

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