Delia tracks a sealed gas through one morning. Its energy rose by 200 J, and she measured 350 J entering as heat. She never measured the work.
The first law finds the missing number. The change in a system's energy equals the energy that enters it minus the energy that leaves it, and any one unknown in that sentence can be worked out from the other two.
Start from what the law says about Delia's gas: the change is +200 J, the energy in is 350 J, and the energy out is unknown.
The gas kept 200 J of the 350 J that entered. The rest left: 350 - 200 = 150, so 150 J left as work.
The three arrangements, one per unknown. Finding the change: change in energy = energy in - energy out.
Finding the energy in: energy in = change in energy + energy out. Everything the system kept plus everything that left had to come in.
Finding the energy out: energy out = energy in - change in energy. Whatever came in and was not kept went back out.
When the energy falls, the change carries a minus sign. A system that drops 40 J while taking in 10 J as heat sent out 10 - (-40) = 50, so 50 J left.
A sealed tub of water gains 110 J of energy while 45 J leaves it as heat. Calculate the energy that entered the tub as work.
Write down the values:
change = +110 J, energy out = 45 J, energy in = ?
Write down the arrangement:
energy in = change in energy + energy out
Substitute in the values, and calculate:
energy in = 110 + 45 = 155
155 J entered the tub as work.
The gas in a sealed cylinder takes in 50 J as heat while its energy falls by 160 J. Calculate the energy that left the gas as work.
Write down the values:
energy in = 50 J, change = -160 J, energy out = ?
Write down the arrangement:
energy out = energy in - change in energy
Substitute in the values, and calculate:
energy out = 50 - (-160) = 210
210 J left the gas as work.
A sealed gas's energy rises by 80 J while it takes in 260 J as heat. Enter the energy that left the gas as work, in J.
The water in a sealed boiler gains 130 J of energy while 55 J leaves it as heat. Enter the energy that entered the water as work, in J.
A sealed pouch of soup's energy falls by 90 J while the pouch takes in 30 J as heat. Enter the energy that left the pouch as work, in J.
A sealed cylinder of gas takes in 410 J as heat and does 175 J of work. Enter the change in the gas's energy in J.
The air in a sealed mattress gains 75 J of energy while 20 J leaves it as heat. Enter the energy that entered the air as work, in J.
A sealed plastic bag of air takes in 45 J as heat from a heating vent's warm air while it does 110 J of work swelling against the air around it. Enter the change in the bag's energy in J. Use a minus sign if the energy decreases.
The air sealed in an inflatable kayak gains 125 J of energy while Emrys's foot pump does 150 J of work on it. Enter the energy that left the kayak's air as heat, in J.
A pump stirs the water in a sealed storage tank, doing work on it. Over an hour, 320 J leaves the water as heat and the water's energy falls by 260 J. Enter the energy the pump put in as work, in J.
During a morning, the air sealed under a terrarium's flexible cover takes in 270 J as heat through the glass and does 38 J of work raising the cover. Enter the change in the air's energy in J.