Some propane occupies 150 cm^3 at 12.4°C. Find the temperature when its volume is 132ft^3 if the pressure remains constant.
To find the temperature when the volume changes, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas (which remains constant)
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature of the gas in kelvin
First, we need to convert the given volume of 132 ft^3 to the proper unit, cm^3, as the initial volume is given in cm^3.
1 ft^3 is equal to 28,316.8466 cm^3. So, the volume of 132 ft^3 is:
V = 132 ft^3 * 28,316.8466 cm^3/ft^3 ≈ 3,730,970 cm^3
We can now plug in the values into the equation:
150 cm^3 * T1 = 3,730,970 cm^3 * T2
Simplifying the equation, we get:
T2 = (150 cm^3 / 3,730,970 cm^3) * T1
Now we need to convert the temperature from Celsius to Kelvin. The Kelvin temperature scale is obtained by adding 273.15 to the Celsius temperature.
So, the initial temperature of 12.4°C in Kelvin is:
T1 = 12.4°C + 273.15 ≈ 285.55 K
Finally, we substitute the values into the equation:
T2 = (150 cm^3 / 3,730,970 cm^3) * 285.55 K
Calculating T2, we find:
T2 ≈ (0.0000402) * 285.55 K ≈ 0.0115 K
Hence, when the volume of the propane is 132 ft^3 and the pressure remains constant, the temperature is approximately 0.0115 K.