A fixed mass of gas of volume 600cm3 at a temperature of 27oC is cooled at constant pressure to a temperature of 0oC. What is the change in volume?

A fixed mass of gas of volume 600cm³ at a temperature of 27^oC is cooled at constant pressure to a temperature of 0^oC. What is the change in volume?

Answer Details

We can use the combined gas law to solve this problem. The combined gas law states that the product of pressure and volume is directly proportional to the product of temperature and the number of moles of gas, assuming constant mass. Mathematically, this can be written as: P₁V₁/T₁ = P₂V₂/T₂ where P is pressure, V is volume, T is temperature, and the subscripts 1 and 2 refer to the initial and final states, respectively. We are told that the initial volume V₁ is 600 cm³ and the initial temperature T₁ is 27^oC = 300K. We also know that the pressure P remains constant throughout the process, and that the final temperature T₂ is 0^oC = 273K. We can solve for the final volume V₂: P₁V₁/T₁ = P₂V₂/T₂ V₂ = (P₁/P₂) * (T₂/T₁) * V₁ Since the pressure is constant, we can cancel it out, and substitute in the given values: V₂ = (273K/300K) * 600 cm³ = 546 cm³ Therefore, the change in volume is 600 cm³ - 546 cm³ = 54 cm³. So, the correct answer is 54 cm³.