an ideal gas occupies a volume of 22.4litres at stp while absorbing 2.53KJ of heat from the surrounding the gas expands isobarically to 32.4 litres. What is the change in internal energy
delta U = Q - W and W in this case = P delta V. Use standard pressure, change in V is given and heat added is given.
To find the change in internal energy, we need to consider the energy transferred as heat and the work done on or by the gas.
Given:
Initial volume (V1) = 22.4 liters
Final volume (V2) = 32.4 liters
Heat absorbed (Q) = 2.53 kJ
At constant pressure (isobaric process), the work done (W) can be calculated using the formula:
W = P * ΔV
where P is the constant pressure and ΔV is the change in volume.
Since the pressure is not given, we need some additional information to calculate the work done. However, we can calculate the change in internal energy (ΔU) using the First Law of Thermodynamics:
ΔU = Q - W
So, if we can find the work done (W), we can determine the change in internal energy (ΔU).
To determine the change in internal energy of an ideal gas, we need to use the First Law of Thermodynamics, which states that the change in internal energy (ΔU) is equal to the heat added (Q) minus the work done by the gas (W).
ΔU = Q - W
Since the gas undergoes an isobaric (constant pressure) process, we can determine the work done using the equation:
W = PΔV
Where P is the pressure and ΔV is the change in volume. In this case, we have the initial volume (V1 = 22.4 L) and the final volume (V2 = 32.4 L).
First, let's convert the given volume values from liters to cubic meters:
V1 = 22.4 L = 0.0224 m³
V2 = 32.4 L = 0.0324 m³
At standard temperature and pressure (STP), the pressure is 1 atmosphere (atm) or 101.3 kPa.
Now, we can calculate the work done:
W = PΔV = (101.3 kPa) * (0.0324 m³ - 0.0224 m³)
W = 101.3 kPa * 0.01 m³
W = 1.013 kJ
Next, we can calculate the change in internal energy (ΔU) by subtracting the work done (W) from the heat added (Q):
ΔU = Q - W = 2.53 kJ - 1.013 kJ
ΔU = 1.517 kJ
Therefore, the change in internal energy is 1.517 kJ (rounded to three decimal places).