Answer:
To determine the pressure change when a constant volume of gas is cooled from 40°C to 20°C, we can use the ideal gas law, which relates the pressure, volume, temperature, and number of moles of a gas:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
Since we are dealing with a constant volume of gas, we can simplify the ideal gas law to:
P1/T1 = P2/T2
where P1 and T1 are the initial pressure and temperature, and P2 and T2 are the final pressure and temperature.
Converting the temperatures to Kelvin:
T1 = 40°C + 273.15 = 313.15 K
T2 = 20°C + 273.15 = 293.15 K
Substituting the values into the equation:
10 atm / 313.15 K = P2 / 293.15 K
Solving for P2:
P2 = (10 atm / 313.15 K) x 293.15 K
P2 = 9.354 atm
Therefore, the pressure of the gas decreases from 10 atm to 9.354 atm when cooled from 40°C to 20°C at constant volume.