A system contains 0.15 m3 of a gas at a pressure of 3.8 bar and 150 C. It is expanded adiabatically till the pressure falls to 1 bar. The gas is then heated at a constant pressure till its change in enthalpy is 70 kJ. Determine the total work done.
To determine the total work done, we need to calculate the work done during the adiabatic expansion and the work done during the constant pressure heating separately, and then sum them up.
1. Work done during adiabatic expansion:
During an adiabatic process, the relation between pressure (P) and volume (V) is given by the following equation:
P1 * V1^γ = P2 * V2^γ
Where P1 and V1 are the initial pressure and volume, P2 and V2 are the final pressure and volume, and γ is the heat capacity ratio of the gas.
Given:
P1 = 3.8 bar (convert to Pa by multiplying by 10^5: 3.8 * 10^5 Pa)
V1 = 0.15 m^3
P2 = 1 bar (convert to Pa: 1 * 10^5 Pa)
To find V2, we rearrange the equation:
V2 = (P1 * V1^γ / P2)^(1/γ)
First, we need to know the value of γ for the gas. γ depends on the type of gas and can be found in tables or given in the problem statement.
Once we have the value of γ, we substitute the given values into the equation to find V2.
2. Work done during constant pressure heating:
The work done during constant pressure heating is given by the equation:
Work = Change in enthalpy (ΔH)
Given:
ΔH = 70 kJ (convert to J: 70 * 1000 J)
This equation assumes that the gas behaves ideally and that there are no other forms of work involved, such as expansion or compression.
After calculating the work done during both processes, we sum them up to find the total work done.