Counting kinetic, potential, and thermal energy, under which condition does a system's total energy stay constant?
Earlier in the course, the full energy account balanced for one special case: with every store counted, the total energy of a system that no energy enters or leaves stays constant. Most systems are not that special case.
Energy enters and leaves real systems all day. What happens to the total then? Keep a ledger, the way a bank tracks an account: deposits in, withdrawals out.
Take a sealed gas as the system. In one minute, 100 J enters it as heat, and the gas does 30 J of work on its surroundings, so 30 J leaves.
Deposits minus withdrawals: 100 - 30 = 70, so the gas ends the minute with 70 J more energy than it started with.
No energy appeared from nowhere, and none vanished. In earlier grades you saw that energy is never created or destroyed, only transferred or transformed.
The law reads totals. Count every transfer that enters, whatever door it used, and count every transfer that leaves; then subtract.
When more energy leaves than enters, the subtraction comes out negative, and the system's energy drops by the gap.
A sealed pouch of air takes in 180 J as heat while it does 55 J of work on its surroundings. Calculate the change in the pouch's energy.
Write down the values:
energy in = 180 J (heat), energy out = 55 J (work), change = ?
Write down the rule:
change in energy = energy in - energy out
Substitute in the values, and calculate:
change = 180 - 55 = 125
The pouch's energy rises by 125 J: the change is +125 J.
A sealed cylinder of gas takes in 45 J as heat while it does 165 J of work on the piston. Calculate the change in the gas's energy.
Write down the values:
energy in = 45 J (heat), energy out = 165 J (work), change = ?
Write down the rule:
change in energy = energy in - energy out
Substitute in the values, and calculate:
change = 45 - 165 = -120
The gas's energy falls by 120 J: the change is -120 J.
A sealed tank of air takes in 250 J as heat and does 90 J of work on its surroundings. Enter the change in the tank's energy in J.
The old special case still sits inside the law. If no energy enters or leaves, the change is zero, and the total stays constant.
In one hour, a system takes in 75 J as heat and releases 75 J as work. What happens to the system's energy over the hour?
Emrys says: 'A system that takes in more energy than it releases ends up with more energy than it started with.' Is Emrys correct?
The gas sealed in a piston cylinder releases 5200 J as heat to the cooling water around it, while the piston does 800 J of work on the gas. Enter the change in the gas's energy in J. Use a minus sign if the energy decreases.
The water sealed in a home radiator loop takes in 340 J as heat at the boiler, takes in 150 J as work from the circulating pump, and releases 260 J as heat to the room air. Enter the change in the water's energy in J.
Over one afternoon, a system releases more energy than it takes in. By the first law of thermodynamics, what happens to the system's energy?