a cylinder with movable piston contains 40 moles of an ideal gas it is placed in an ice water bath where it reach thermal equilibrium. it is then compressed slowly with 7500 j of work done to compress it to a smaller volume. how much does its internal energy change
To find the change in internal energy of the gas in the cylinder, we can use the First Law of Thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat (Q) added to the system minus the work (W) done by the system:
ΔU = Q - W
In this case, the cylinder reaches thermal equilibrium in an ice water bath, implying that no heat is exchanged between the system (gas) and the surroundings. Therefore, Q = 0. Hence, the equation becomes:
ΔU = 0 - W
Now, we know the work (W) done to compress the gas is 7500 J. Substituting the value into the equation, we get:
ΔU = 0 - 7500 J
Therefore, the change in internal energy of the gas in the cylinder is -7500 J.