a piston performs work of 210. L atm on the surroundings, while the cylinder in which it is placed expands from 10. L to 25L. at the same time, 45J of heat is transferred from the surroundings to the system. Against what pressure was the piston working?
Please Explain!
troll
To determine the pressure against which the piston was working, we need to use the first law of thermodynamics, which states that the change in internal energy of a system is equal to the heat transferred to the system minus the work done by the system.
The equation for the first law of thermodynamics is:
ΔU = Q - W
Where:
- ΔU is the change in internal energy of the system
- Q is the heat transferred to the system
- W is the work done by the system
In this case, we have the following information:
ΔU = 0 (since the problem does not mention any change in internal energy)
Q = -45J (negative because heat is transferred from the surroundings to the system)
W = -210 L atm (negative because work is done by the system on the surroundings)
Now, we can plug these values into the equation to solve for the work done by the system:
0 = -45 - (-210)
Simplifying the equation:
0 = -45 + 210
0 = 165
This equation tells us that the work done by the system is equal to 165 L atm. Since work is defined as the force exerted on an object multiplied by the distance over which the force is applied, we can write the equation:
Work = Force × Distance
In this case, the distance is the change in volume of the cylinder, which is (25 L - 10 L) = 15 L. Therefore, we can rewrite the equation:
165 L atm = Force × 15 L
Now we can solve for the force:
Force = 165 L atm / 15 L
Force ≈ 11 L atm
Thus, the piston was working against a pressure of approximately 11 L atm.