3 moles of argon gas initially at a temperature of 20º C, occupy
a volume of 10 liters. The gas undergoes an expansion at constant pressure to a volume of 20 L; then expands adiabatically until it returns to its initial temperature. a) Plot the process on aPV diagram. Calculate: b) the amount of heat that was given to the gas throughout the process, c) the total change in the internal energy of the gas,d) the total work done during the process, e) the final volume of the gas.
To answer this question, we need to apply the concepts of thermodynamics and gas laws. Let's break down the problem step by step:
a) Plotting the process on a PV diagram:
- The initial conditions are given as 3 moles of argon gas, initial temperature of 20º C, and an initial volume of 10 liters.
- The gas undergoes an expansion at constant pressure to a volume of 20 liters. This corresponds to an isobaric process on the PV diagram. On the diagram, you would draw a horizontal line from the initial point (10 L, P) to the final point (20 L, P).
- After the constant pressure expansion, the gas expands adiabatically until it returns to its initial temperature. This corresponds to an adiabatic process on the PV diagram. On the diagram, you would draw a curve connecting the final point of the isobaric process to the point with the same temperature as the initial point.
b) Calculating the amount of heat given to the gas throughout the process:
- Since the expansion from 10 L to 20 L is at constant pressure, the heat transfer can be calculated using the equation Q = ΔH = nCpΔT, where Q is the heat transfer, ΔH is the change in enthalpy, n is the number of moles of gas, Cp is the molar heat capacity at constant pressure, and ΔT is the change in temperature.
- First, convert the initial temperature from Celsius to Kelvin by adding 273.15: 20º C + 273.15 = 293.15 K.
- Calculate the change in temperature: ΔT = Tf - Ti = 293.15 K - 293.15 K = 0 K (since the final and initial temperatures are the same).
- Calculate the amount of heat transferred: Q = 3 moles * Cp * ΔT.
c) Calculating the total change in internal energy of the gas:
- The total change in internal energy (ΔU) can be calculated using the first law of thermodynamics, which states that ΔU = Q - W, where Q is the heat transfer and W is the work done by the gas.
- We already calculated Q in the previous step. To calculate W, we need to determine the work done during the process.
d) Calculating the total work done during the process:
- Since the expansion from 10 L to 20 L is at constant pressure, the work done can be calculated using the equation W = PΔV, where P is the pressure and ΔV is the change in volume.
- First, we need to determine the pressure. The problem states that the process occurs at constant pressure, but does not provide the actual value. If the pressure is not given explicitly, it is not possible to calculate the total work done without further information.
e) Calculating the final volume of the gas:
- The final volume of the gas is given as 20 liters, as specified in the problem statement.
In summary, you can plot the process on a PV diagram, but you would need the actual pressure value to calculate the amount of heat transferred (b), the total change in internal energy (c), and the total work done during the process (d). The final volume of the gas is given as 20 liters (e).