FULL REVIEW
Full Review — First Law of Thermodynamics — Algebra-Based
Review the essential ideas, relationships, and problem-solving tools for First Law of Thermodynamics.
TIME
45–60 minutes
BEST FOR
A complete unit review
FINISH WITH
A readiness check
After this full review, you'll be able to...
recall the essential ideas, apply them to representative problems, and determine what to study next.
Choose how you want to review
Course Alignment
This Physics Sensei Unit Review is an independent learning resource. Use it to reinforce key concepts, prepare for homework, or review before a quiz or exam.
RESOURCE: Physics Sensei Unit Review | UNIT ID: THM-U08 | TOPIC: First Law of Thermodynamics | COURSE LEVEL: Algebra-Based
BEST USED ✓ After learning the unit ✓ Before starting homework ✓ Before a quiz or exam
Your Review Plan
Complete these six stages in order. Each stage builds on the previous one and prepares you for the final readiness check.
6 Stages • Approximately 45–60 minutes.
Warm-Up Check
Before you begin, take a moment to see what you already remember. Do not worry about getting everything right. This is only a starting point.
ACTIVITY 1
Recall Activity 1
Apply the sign convention
For W defined as work done by the system, assign signs when a gas absorbs 420 J and is compressed with 160 J of work done on it.
Reveal Answers
Q = +420 J and W = -160 J.
Why it works: Work done on the system corresponds to negative work done by the system.
ACTIVITY 2
Recall Activity 2
Rearrange the first law
Rearrange ΔU = Q - W to solve for Q.
Reveal Answers
Q = ΔU + W.
Why it works: Move -W to the other side.
ACTIVITY 3
Recall Activity 3
PV work units
Show that Pa·m³ has units of joules.
Reveal Answers
Pa·m³ = (N/m²)m³ = N·m = J.
Why it works: Pressure-volume work is an energy.
Ready to strengthen your understanding?
You've refreshed what you already know. Next, you'll reinforce the essential concepts that will help you solve problems with confidence. Need to see the learning path again?
Core Concepts
Let's rebuild the key ideas one step at a time. Focus on understanding the relationships before worrying about solving problems.
KEY CONCEPT 1
First-Law Energy Balance
Use ΔU = Q - W with W as work done by the system. Q > 0 for heat absorbed, Q < 0 for heat released, W > 0 for expansion work, and W < 0 when work is done on the system.
ΔU = Q − W
Example: If Q = 900 J and W = 350 J, ΔU = 550 J.
Sensei note: Write the signs before inserting numbers.
KEY CONCEPT 2
State Function vs. Path Transfers
Internal energy U is a state function: ΔU depends only on initial and final states. Q and W depend on the process path, even though Q - W must equal the same ΔU between fixed endpoints.
ΔU = U₂ − U₁ (path independent)
Example: Two paths can have different Q and W but the same ΔU.
Sensei note: Do not treat Q or W as properties of a state.
KEY CONCEPT 3
Pressure-Volume Work
For constant external pressure, W = P ΔV. More generally, work is associated with the area under a P-V path. Expansion gives positive work by the gas.
W = PΔV (constant pressure)
Example: At 2.5 × 10⁵ Pa, an expansion of 3.0 × 10⁻³ m³ gives W = 750 J.
Sensei note: Convert liters to cubic meters before multiplying by pressure.
Ready to apply these ideas?
You've reinforced the essential concepts. Now it's time to put them into practice by working through guided examples and building your problem-solving confidence. Need a quick reminder?
Guided Practice
Now it's time to apply what you've reviewed.
Work through each activity in order. The examples become gradually more challenging, and each one prepares you for the final readiness check.
PRACTICE 1
Worked Example
A gas absorbs 1.20 kJ and does 450 J of work. Calculate ΔU.
Convert 1.20 kJ to 1200 J and apply ΔU = Q - W.
Reveal Answers
ΔU = 1200 J - 450 J = 750 J.
Why it works: Keep all energy quantities in the same unit.
PRACTICE 2
Guided Problem
A gas is compressed at constant pressure 1.8 × 10⁵ Pa from 6.0 L to 3.5 L while 220 J of heat leaves the gas. Find ΔU.
Compute ΔV = -2.5 L = -2.5 × 10⁻³ m³, then W = P ΔV.
Reveal Answers
W = -450 J; Q = -220 J; ΔU = -220 - (-450) = 230 J.
Why it works: Compression makes W negative in the work-by-system convention.
PRACTICE 3
Independent Problem
A process raises internal energy by 500 J while the gas expands from 2.0 L to 5.0 L at 1.0 × 10⁵ Pa. Find Q.
Find W = P ΔV, then use Q = ΔU + W.
Reveal Answers
W = 300 J; Q = 800 J.
Why it works: Heat input supplies both the internal-energy increase and expansion work.
Ready to check your understanding?
You've practiced the essential skills with guidance. Now it's time to solve a few short problems on your own and confirm you're ready to move forward. Need a quick reminder?
Confidence Check
You've rebuilt the key ideas and practiced them with guidance. Now try these short questions on your own to check your understanding before moving on.
QUICK CHECK 1
Compression balance
Solve using the first law and the stated sign convention.
Q = -100 J and W = -350 J. Find ΔU.
Reveal Answers
ΔU = 250 J.
Why it works: ΔU = -100 - (-350).
QUICK CHECK 2
Solve for work
Solve using the first law and the stated sign convention.
Q = 700 J and ΔU = 480 J. Find W.
Reveal Answers
W = 220 J.
Why it works: W = Q - ΔU.
QUICK CHECK 3
PV work
Solve using the first law and the stated sign convention.
A gas expands 4.0 L at 2.0 × 10⁵ Pa. Find W.
Reveal Answers
W = 800 J.
Why it works: 4.0 L = 4.0 × 10⁻³ m³, so W = P ΔV.
How did it go?
You've checked your understanding. Take one final look at the essential ideas before deciding what to do next. Need a quick reminder?
Summary
Before moving on, take one final look at the most important ideas from this review.
KEY TAKEAWAY 1
First-law equation
ΔU = Q - W with W defined as work done by the system.
KEY TAKEAWAY 2
State and path
ΔU is state-dependent only; Q and W depend on the process.
KEY TAKEAWAY 3
PV calculations
Use W = P ΔV at constant pressure and track the sign of ΔV.
Ready for your next step?
You've reviewed the essential ideas one last time. Now choose the resource that best matches how confident you feel. Need a quick reminder?
Next Step
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