The pressure of a gas in a constant volume gas thermometer is 80cm Hg in melting ice at 1atm.when the bulb is placed in a liquid the pressure becomes 160cm of Hg find the temperature of liquid

To determine the temperature of the liquid using the information provided from the constant volume gas thermometer, we can apply the principles of gas laws, specifically the relationship between pressure and temperature. In this case, we will use the concept of absolute temperature, which is measured in Kelvin.

Understanding the Basics

In a constant volume gas thermometer, the pressure of the gas is directly proportional to its temperature when the volume is held constant. This relationship can be expressed mathematically as:

P1/T1 = P2/T2

Where:

• P1 = initial pressure of the gas
• T1 = initial temperature (in Kelvin)
• P2 = final pressure of the gas
• T2 = final temperature (in Kelvin)

Given Values

From the problem, we know:

• The pressure in melting ice (1 atm) corresponds to 80 cm Hg.
• The pressure in the liquid is 160 cm Hg.

Converting Pressures

First, we need to convert the pressures into a consistent unit. Since we are using cm Hg, we can keep them as is:

• P1 = 80 cm Hg
• P2 = 160 cm Hg

Finding the Initial Temperature

The temperature at which the pressure is 80 cm Hg (melting ice) is 0°C, which is equivalent to:

T1 = 0°C + 273.15 = 273.15 K

Setting Up the Equation

Now we can substitute the known values into the equation:

80 cm Hg / 273.15 K = 160 cm Hg / T2

Solving for T2

To find T2, we can rearrange the equation:

T2 = (160 cm Hg * 273.15 K) / 80 cm Hg

Calculating this gives:

T2 = (160 * 273.15) / 80

T2 = 43224 / 80

T2 = 540.3 K

Final Temperature Conversion

To convert this temperature back to Celsius, we subtract 273.15:

T2 (in °C) = 540.3 K - 273.15 = 267.15°C

Conclusion

The temperature of the liquid, when the pressure in the gas thermometer reaches 160 cm Hg, is approximately 267.15°C. This calculation illustrates how pressure changes in a gas can be used to determine temperature, showcasing the direct relationship between these two physical properties in a controlled environment.