Question

A cycle pump contains 50cm³ of air at 17°C and a pressure of 1 atm. Find the pressure when the air is compressed to 10cm³ and the temperature rises to 27°C?

Answer 1

To find the pressure when the air is compressed and the temperature rises, we can use the ideal gas law equation: PV = nRT. First, convert the temperatures from Celsius to Kelvin. Then, use the equation n = PV / RT to find the initial number of moles (n) of gas. Finally, plug in the values into the equation P = (nRT) / V to find the final pressure.

Step-by-step explanation:

To find the pressure when the air is compressed and the temperature rises, we can use the ideal gas law equation: PV = nRT. Here, P represents pressure, V represents volume, n represents the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.

First, we need to convert the temperatures from Celsius to Kelvin by adding 273. So, the initial temperature is 17 + 273 = 290K, and the final temperature is 27 + 273 = 300K.

Next, we need to find the initial number of moles (n) of gas. We can use the equation PV = nRT and rearrange it to n = PV / RT. Plugging in the initial values, we get n = (1 atm x 50cm³) / (0.0821 atm L/mol K x 290K) = 2.1 x 10^-3 mol.

Now, we can use the same equation to find the final pressure. Plugging in the final values, we get P = (2.1 x 10^-3 mol x 0.0821 atm L/mol K x 300K) / 10cm³ = 0.518 atm.