The pressure of the gas in a constant volume gas thermometer is 70kPa at the ice point.Find the pressure at the steam point.

To find the pressure of the gas at the steam point using a constant volume gas thermometer, we can apply the principles of gas laws, particularly Gay-Lussac's Law. This law states that the pressure of a gas is directly proportional to its absolute temperature when the volume is held constant. In this case, we need to know the pressures at two reference points: the ice point (0 degrees Celsius) and the steam point (100 degrees Celsius).

Understanding the Relationship Between Pressure and Temperature

First, let's establish the temperatures in Kelvin, as gas laws require absolute temperatures. The conversion from Celsius to Kelvin is done by adding 273.15:

• Ice point: 0 °C = 273.15 K
• Steam point: 100 °C = 373.15 K

Now, we know that at the ice point, the pressure is 70 kPa. We can set up a proportion based on Gay-Lussac's Law:

Setting Up the Proportion

The relationship can be expressed as:

P1 / T1 = P2 / T2

Where:

• P1 = pressure at the ice point (70 kPa)
• T1 = absolute temperature at the ice point (273.15 K)
• P2 = pressure at the steam point (unknown)
• T2 = absolute temperature at the steam point (373.15 K)

Calculating the Pressure at the Steam Point

Now we can rearrange the equation to solve for P2:

P2 = P1 × (T2 / T1)

Substituting the known values:

P2 = 70 kPa × (373.15 K / 273.15 K)

Calculating the fraction:

P2 = 70 kPa × 1.366

Now, performing the multiplication:

P2 ≈ 95.62 kPa

Final Result

Therefore, the pressure of the gas at the steam point is approximately 95.62 kPa. This calculation illustrates how the pressure of a gas increases with temperature when the volume remains constant, demonstrating the direct relationship described by Gay-Lussac's Law.