an ideal system absorbed some amount of heat and gas expand and the piston move to 0.4 meter against than the atmospheric pressure. If the cross sectional area of the container is 0.6 meter2. What is the amount of heat absorbed?
To determine the amount of heat absorbed by the system, we can use the First Law of Thermodynamics, which relates the change in internal energy of the system (ΔU), the heat added or removed (Q), and the work done (W):
ΔU = Q - W
In this case, the system absorbs heat and does work. The work done is given by:
W = F * d
Where F is the Force exerted on the piston and d is the distance moved by the piston.
Given that the piston moves 0.4 meters against the atmospheric pressure, we can calculate the work done as follows:
W = F * d
W = P * A * d
Where P is the atmospheric pressure and A is the cross-sectional area of the container.
Now, since the piston moves against the atmospheric pressure, the force exerted by the piston must be equal to the atmospheric pressure multiplied by the cross-sectional area:
F = P * A
Substituting this equation into the work equation, we get:
W = (P * A) * d
Now we can substitute the given values:
W = (atmospheric pressure) * (cross-sectional area) * (distance moved)
W = (P) * (A) * (d)
W = (1 atm) * (0.6 m^2) * (0.4 m)
Finally, we can calculate the work done by multiplying the given values:
W = (1) * (0.6) * (0.4) = 0.24 Joules
The amount of heat absorbed by the system can now be calculated by rearranging the First Law of Thermodynamics equation:
Q = ΔU + W
Since the problem states that the system absorbs heat, the change in internal energy (ΔU) should be positive. Therefore:
Q = ΔU + W
Q = 0 + 0.24 J
Q = 0.24 Joules
So, the amount of heat absorbed by the system is 0.24 Joules.