A burner warms a sealed metal cylinder of gas: 500 J enters the gas as heat. At the same time the gas does work on its piston, and 120 J leaves.
How much better off is the gas? The first law of thermodynamics already says: the change in a system's energy equals the energy that enters it minus the energy that leaves it. This lesson turns that sentence into a routine.
Label each flow first, door by door. The burner's transfer is heat, and it enters: energy in = 500 J.
The piston transfer is work, and it leaves: energy out = 120 J.
Subtract: 500 - 120 = 380, so the gas gains 380 J.
As a word equation: change in energy = energy in - energy out.
A negative answer is allowed. When more energy leaves than enters, the change comes out negative, and the system's energy falls by that amount.
A sealed balloon of air takes in 700 J as heat from a hot parking lot while it swells, doing 260 J of work on the outside air. Calculate the change in the balloon's energy.
Write down the values:
energy in = 700 J (heat), energy out = 260 J (work), change = ?
Write down the equation:
change in energy = energy in - energy out
Substitute in the values, and calculate:
change = 700 - 260 = 440
The balloon's energy rises by 440 J: the change is +440 J.
A sealed flexible pack of juice releases 190 J as heat into a cooler while the ice pressing on it does 60 J of work on it. Calculate the change in the juice's energy.
Write down the values:
energy in = 60 J (work), energy out = 190 J (heat), change = ?
Write down the equation:
change in energy = energy in - energy out
Substitute in the values, and calculate:
change = 60 - 190 = -130
The juice's energy falls by 130 J: the change is -130 J.
The air sealed in a soccer ball takes in 420 J as heat on a hot field while it does 180 J of work swelling the ball's skin outward. Enter the change in the energy of the ball's air, in J.
A sealed pot of stew on a cold porch releases 310 J as heat while Birta turns a crank paddle inside it, doing 40 J of work on the stew. Enter the change in the stew's energy in J. Use a minus sign if the energy decreases.
The gas sealed in a spray can takes in 95 J as heat from a warm shelf while it does 25 J of work bulging the can's base outward. Enter the change in the gas's energy in J.
Overnight, a sealed tub of bread dough takes in 110 J as heat from a warm kitchen while the rising dough does 35 J of work lifting the tub's lid. Enter the change in the dough's energy in J.
Delia kneads a sealed hand warmer, doing 85 J of work on it, while it releases 640 J as heat to her cold hands. Enter the change in the warmer's energy in J. Use a minus sign if the energy decreases.
In a science demo, the air sealed in a clear box takes in 120 J as heat from a heating pad and 35 J as work from a plunger, while it releases 65 J as heat through the box's cold back wall. Enter the change in the air's energy in J.