If a quantity of gas in a piston cylinder has a volume of 0.9 m3 and is initially at room temperature (30°C) and is heated in an isobaric (constant-pressure) process, what will be the temperature of the gas in degrees Celsius when it has expanded to a volume of 1.2 m3?
assuming the gas is ideal, we can use Charles' Law:
V1/T1 = V2/T2
where
V1 = initial volume
V2 = final volume
T1 = initial temperature (in Kelvin)
T2 = final temperature (in Kelvin)
we first convert the given temp to Kelvin:
T1 = 30 + 273.15 = 303.15 K
substituting,
V1/T1 = V2/T2
0.9 / 303.15 = 1.2 / (T2)
T2 = 1.2*303.15/0.9
T2 = 404.2 K or 131.05 deg C
hope this helps~ :)
To find the final temperature of the gas in the given process, we need to use the ideal gas law formula, which states:
PV = nRT
Where:
P = pressure of the gas (constant in this case, as it is an isobaric process)
V = volume of the gas
n = number of moles of gas
R = ideal gas constant
T = temperature of the gas
Since the pressure is constant, we can rewrite the formula as:
V/T = nR/P
Now, let's solve the equation using the initial and final volumes of the gas:
V1/T1 = V2/T2
Substituting the provided values:
0.9 m^3 / (30°C + 273.15) K = 1.2 m^3 / T2
Simplifying, we can write:
0.9 / (30 + 273.15) = 1.2 / T2
Calculating the left side:
0.9 / 303.15 ≈ 0.0029721
Now, rearranging the equation to solve for T2:
T2 = (1.2 / 0.0029721)
Calculating the right side:
T2 ≈ 403.5801
Therefore, the final temperature of the gas, when it has expanded to a volume of 1.2 m^3, is approximately 403.58°C.