A gas sample with an initial volume of 3.25 dm3 is heated and allowed to expand to 9.75 dm3 at constant pressure. What is the ratio of the final absolute te...

A gas sample with an initial volume of 3.25 dm3 is heated and allowed to expand to 9.75 dm3 at constant pressure. What is the ratio of the final absolute temperature to the initial absolute temperature?

Answer Details

The problem involves a gas sample that is heated and allowed to expand at constant pressure. This means that the gas undergoes an isobaric process. According to the ideal gas law, PV = nRT, the volume of a gas is directly proportional to its absolute temperature at constant pressure. Therefore, if the initial volume of the gas is 3.25 dm^3 and the final volume is 9.75 dm^3, then the final absolute temperature must be three times the initial absolute temperature. To see why this is the case, we can rearrange the ideal gas law to solve for temperature: T = PV/nR. Because the pressure and the number of moles of gas are constant, we can say that T1V1 = T2V2, where T1 is the initial absolute temperature and V1 is the initial volume, and T2 is the final absolute temperature and V2 is the final volume. Solving for T2/T1, we get (T2/T1) = V2/V1 = 9.75/3.25 = 3. Therefore, the ratio of the final absolute temperature to the initial absolute temperature is 3:1. Therefore, the answer is: 3:1.