Introduction:
When a gas is heated at constant pressure, its temperature increases. This increase in temperature affects the density of the gas, causing it to change. In this explanation, we will discuss the percentage decrease in density of an ideal gas when the temperature is increased by 10 percent at constant pressure.

Understanding Density:
Density is defined as the mass of a substance per unit volume. For an ideal gas, the density can be calculated using the equation:

Density = (mass of gas) / (volume of gas)

Effect of Temperature on Density:
According to the ideal gas law, the density of an ideal gas is directly proportional to its pressure and inversely proportional to its temperature. Mathematically, it can be expressed as:

Density ∝ (pressure) / (temperature)

When the temperature of a gas increases, its density decreases, assuming the pressure remains constant. This can be explained by the kinetic theory of gases. As the gas molecules gain more energy with increased temperature, they move faster and occupy a larger volume. Consequently, the same mass of gas now occupies a larger volume, resulting in a decrease in density.

Percentage Decrease in Density:
To determine the percentage decrease in density when the temperature is increased by 10 percent, we can use the formula:

Percentage decrease = (initial density - final density) / initial density * 100

Since the initial density is inversely proportional to temperature, we can write:

Initial density ∝ 1 / initial temperature

Similarly, the final density is inversely proportional to the final temperature:

Final density ∝ 1 / final temperature

Using these relations, we can rewrite the percentage decrease formula as:

Percentage decrease = (1 / initial temperature - 1 / final temperature) / (1 / initial temperature) * 100

Conclusion:
When the temperature of an ideal gas is increased by 10 percent at constant pressure, the density of the gas decreases by a certain percentage. This decrease in density can be calculated using the formula mentioned above. It is important to note that this explanation assumes an ideal gas behavior and constant pressure throughout the process.

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