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This question involves the relationship between pressure, volume, and temperature of a gas, which can be understood using the **ideal gas law**:

\[
PV = nRT
\]

where:
- \( P \) is the pressure,
- \( V \) is the volume,
- \( n \) is the number of moles of gas,
- \( R \) is the ideal gas constant, and
- \( T \) is the temperature (in Kelvin).

### Step 1: Temperature change
The temperature is lowered from 39.0°C to 8.0°C. First, we convert these temperatures to Kelvin by adding 273.15:
\[
T_1 = 39.0 + 273.15 = 312.15\,K
\]
\[
T_2 = 8.0 + 273.15 = 281.15\,K
\]

### Step 2: Pressure change
The pressure is increased by 15%, so the new pressure is:
\[
P_2 = 1.15P_1
\]

### Step 3: Use the combined gas law
The combined gas law, which relates the initial and final states of a gas, is:
\[
\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}
\]

Rearranging for \( V_2 \) (the new volume):
\[
V_2 = V_1 \times \frac{P_1}{P_2} \times \frac{T_2}{T_1}
\]

Substitute \( P_2 = 1.15P_1 \) into the equation:
\[
V_2 = V_1 \times \frac{1}{1.15} \times \frac{281.15}{312.15}
\]

### Step 4: Calculate the volume ratio
Let’s compute this to see if the volume increases or decreases.

I'll now calculate it for you.The volume of the nitrogen gas decreases, with the new volume being approximately 78.3% of the original volume.

### Step 5: Percentage change in volume
To calculate the percentage decrease:
\[
\text{Percentage change} = \left( \frac{V_1 - V_2}{V_1} \right) \times 100 = \left( 1 - 0.783 \right) \times 100 = 21.7\%
\]

Thus, the volume of the gas decreases by approximately **22%**.

Would you like more details or have any questions? Here are some related questions to consider:

1. What is the ideal gas law, and how does it relate temperature, pressure, and volume?
2. How does changing pressure affect gas volume if temperature is constant?
3. Why do we need to convert temperatures to Kelvin in gas law calculations?
4. How would the volume change if the temperature was increased instead?
5. Can the ideal gas law be applied to gases at very high pressures or very low temperatures?

**Tip**: Always convert Celsius to Kelvin when working with gas laws to avoid negative temperatures in calculations!

Suppose the temperature of a sample of nitrogen gas is lowered from 39.0°C to 8.0°C, and at the same time the pressure is increased by 15%. Does the volume of the sample increase, decrease, or stay the same? If it changes, calculate the percentage change in volume.

Explore how the volume of nitrogen gas changes when the temperature is lowered from 39°C to 8°C and the pressure increases by 15%. Learn how to apply the ideal gas law and the combined gas law to calculate the percentage change in volume. Suitable for high school physics students.

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