a constant volume gas thermometer using helium records a pressure of p₁ =20.0kpa at triple point of water (273.16k) and a pressure p₂ =14.3 kapa the temperature of dry ice is

To determine the temperature of dry ice using the readings from a constant volume gas thermometer filled with helium, we can apply the principles of gas laws, specifically the relationship between pressure and temperature. In a constant volume system, the pressure of a gas is directly proportional to its absolute temperature. This means that if we know the pressures at two different temperatures, we can find the unknown temperature using a simple ratio.

Understanding the Relationship

The relationship we are using is derived from the ideal gas law, which states that for a given amount of gas at constant volume, the pressure (P) is proportional to the temperature (T) in Kelvin. Mathematically, this can be expressed as:

P1/T1 = P2/T2

Given Values

• P1 = 20.0 kPa (pressure at the triple point of water)
• T1 = 273.16 K (temperature at the triple point of water)
• P2 = 14.3 kPa (pressure at the temperature of dry ice)
• T2 = ? (temperature of dry ice in Kelvin)

Setting Up the Equation

We can rearrange the equation to solve for T2:

T2 = (P2 * T1) / P1

Substituting the Values

Now, let’s plug in the values we have:

T2 = (14.3 kPa * 273.16 K) / 20.0 kPa

Calculating the Temperature

Now we can perform the calculation step by step:

1. Multiply P2 by T1: 14.3 kPa * 273.16 K = 3905.428 kPa·K
2. Now divide by P1: 3905.428 kPa·K / 20.0 kPa = 195.2714 K

Final Result

The temperature of dry ice, T2, is approximately 195.27 K. To convert this to Celsius, we subtract 273.15:

T2 (in °C) = 195.27 K - 273.15 = -77.88 °C

Thus, the temperature of dry ice is around -77.88 °C. This value aligns well with the known sublimation point of dry ice, which is about -78.5 °C at atmospheric pressure, confirming the accuracy of our calculations.