A gas is confined to a cylinder under constant atmospheric pressure, as illustrated in the figure below. When 0.46 kJ of heat is added to the gas, it expands and does 186 J of work on the surroundings. What are the values of ÄH and ÄE for this process?
To find the values of ÄH (change in enthalpy) and ÄE (change in internal energy), we need to use the First Law of Thermodynamics, which states that the change in internal energy (ÄE) of a system is equal to the heat added to the system (Q) minus the work done by the system on the surroundings (W).
The formula is:
ÄE = Q - W
Given that Q = 0.46 kJ of heat is added to the gas, and the gas does 186 J of work on the surroundings, we can substitute these values into the formula to find ÄE.
ÄE = (0.46 kJ) - (186 J)
Before proceeding further, we need to convert both values to the same units. Since ÄE is in joules (J), we'll convert 0.46 kJ to joules.
0.46 kJ = 0.46 × 1000 J = 460 J
Now we can substitute the values:
ÄE = 460 J - 186 J
ÄE = 274 J
Therefore, the change in internal energy (ÄE) for this process is 274 Joules.
To find the change in enthalpy (ÄH), we can use the relationship between enthalpy and internal energy, which is given by the equation:
ÄH = ÄE + PΔV
Here, P is the pressure and ΔV is the change in volume. Since the pressure is constant and the gas expands, the work done by the gas on the surroundings can be written as:
W = -PΔV
Therefore, we can rewrite the equation as:
ÄE = ÄH - PΔV
We already know that ÄE = 274 J, and given that the work done by the gas on the surroundings is 186 J, we can substitute these values:
274 J = ÄH - 186 J
Now we can solve for ÄH:
ÄH = 274 J + 186 J
ÄH = 460 J
Therefore, the change in enthalpy (ÄH) for this process is 460 Joules.