To calculate the final temperature of the gas, we can use the Ideal Gas Law, which states:

$PV = nRT$

Since the volume $V$ and the amount of gas $n$ are constant, we can simplify this relationship to:

$\frac{P_1}{T_1} = \frac{P_2}{T_2}$

Where:

• $P_1$ and $T_1$ are the initial pressure and temperature,
• $P_2$ and $T_2$ are the final pressure and temperature.

Given:

• Initial pressure, $P_1 = 400 \, \text{kPa}$
• Initial temperature, $T_1 = 350 \, \text{K}$
• Final pressure, $P_2 = 150 \, \text{kPa}$

We need to find the final temperature, $T_2$.

Solution:

Rearranging the equation to solve for $T_2$:

$T_2 = T_1 \times \frac{P_2}{P_1}$

Substitute the known values:

$T_2 = 350 \, \text{K} \times \frac{150 \, \text{kPa}}{400 \, \text{kPa}}$

$T_2 = 350 \, \text{K} \times 0.375$

$T_2 = 131.25 \, \text{K}$

Final Answer:

The final temperature of the gas is 131.25 K.

Would you like further clarification, or do you have any additional questions?

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Here are 5 related questions:

1. What happens to the volume of an ideal gas if the temperature is increased while pressure is constant?
2. How does the number of gas molecules affect the pressure of an ideal gas at constant volume and temperature?
3. Can you describe the relationship between pressure and volume at constant temperature (Boyle's Law)?
4. How does the Ideal Gas Law change if we change the gas to a non-ideal gas?
5. What is the effect of temperature on the speed of gas molecules?

Tip: Always ensure to check the units of temperature in gas law problems—they should always be in Kelvin.