If 842 J of heat is needed to increase the temperature of ethane gas (C2H6) in a 15 litre container from 237 K to 400 K, how much gas is in the container
To find the amount of gas in the container, we need to use the ideal gas law.
The ideal gas law is given by the equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant
T is the temperature of the gas in Kelvin
In this case, we are given the temperature, volume, and the amount of heat absorbed by the gas. We can use the heat absorbed to calculate the change in temperature, and then use the change in temperature to find the final temperature.
First, let's find the change in temperature:
Heat absorbed = nCΔT
Where C is the heat capacity of the gas at constant volume.
In this case, we are given the heat absorbed (842 J) and the initial temperature (237 K). We need to find the change in temperature, ΔT.
ΔT = Heat absorbed / (nC)
Since we are given the volume (15 L) and the initial and final temperatures, we can use the ideal gas law to find the number of moles of gas, n.
PV = nRT
n = PV / RT
Let's substitute the given values into the equation and calculate the number of moles of gas.
n = (15 L) * (P) / (R * 237 K)
Now that we have the number of moles of gas, we can calculate the change in temperature.
ΔT = 842 J / (n * C)
Lastly, we can find the final temperature by adding the initial temperature to the change in temperature.
Final Temperature = Initial Temperature + ΔT
Now let's substitute the given values into the equations and calculate the amount of gas in the container.