Foundations — First law of thermodynamics — dU = dQ − dW, sign conventions

1.7.13 · D1 · Physics › Thermodynamics › First law of thermodynamics — dU = dQ − dW, sign conventions

Yeh page parent note mein use hone wale har symbol ko bilkul zero se build karta hai. Hum dependency order mein jaate hain: har idea sirf upar define kiye gaye concepts use karta hai. Agar baad mein koi letter samajh na aaye, toh woh pehle yahan define kiya gaya tha.

0. The system — hum dekh kya rahe hain?

Kisi bhi symbol se pehle, humein ek cheez chahiye jo hum dekhein. Thermodynamics mein woh cheez ek system hoti hai: matter ka ek chosen tukda — yahan, ek cylinder mein band gas jisme movable piston hai. Universe ki baaki sab cheez surroundings hai.

Figure dekho: dashed pale-yellow line boundary hai. Neeche ki flame se heat andar aati hai; upar ka piston slide kar sakta hai, gas ko bahar push karne deta hai. Energy sirf inhi do tareekon se move karti hai — yeh poora law ek picture mein hai.

1. $P$ — pressure

Topic ko yeh kyun chahiye: gas kaam karti hai piston ko push karke, aur "push" exactly force hai. Push ko ek number mein badhalne ke liye hum pressure use karte hain. Units: pascals, $\text{Pa}=\text{N}/{\text{m}}^2$.

2. $V$ — volume

Topic ko yeh kyun chahiye: jab piston move karta hai, jagah badal jaati hai. Space mein woh change hi woh tarika hai jisse gas energy kharach karti hai. Isliye volume woh quantity hai jiske change ko hum sabse zyada dekhenge.

3. $T$ — temperature

Topic ko yeh kyun chahiye: ideal gas ke liye, "zyada garam" aur "zyada internal energy" ek hi baat hai. Temperature, internal energy ka reader-friendly face hai. Deep version ke liye dekho Internal energy and degrees of freedom.

4. State, aur triplet $(P,V,T)$

Topic ko yeh kyun chahiye: internal energy ki star property — ki woh sirf state par depend karti hai, journey par nahi — "state" word ke bina boli hi nahi ja sakti. Yeh poore note ka hinge hai.

5. State function vs path function — lake ki picture

Yeh distinction sabko confuse karti hai, isliye iski apni figure hai.

Figure mein, dono blue paths same do dots se shuru aur khatam hoti hain (same state change) lekin neeche alag areas sweep karti hain. Internal energy $U$ (level) same rehti hai; heat $Q$ aur work $W$ (baarish aur outflow, ∝ swept areas) nahi rehte.

6. $U$ — internal energy

Topic ko yeh kyun chahiye: yeh "stored" bucket hai. Heat jo andar aaye aur work ke roop mein na nikle, yahan land karni chahiye — $U$ badhegi, yani $T$ badhegi. First Law ka poora point is bucket ko track karna hai. Internal energy and degrees of freedom mein aur detail hai.

7. $Q$ — heat

Topic ko yeh kyun chahiye: heat input channel hai — "khaaya gaya khaana." $Q$ ke bina gas bahar se energy kabhi gain nahi kar sakti bina push kiye. Temperature se alag: temperature ek state hai (kitna hot); heat ek transfer hai (energy move ho rahi hai).

8. $W$ — work (gas ke dwara kiya gaya), aur $dW=PdV$

Ab hum crucial formula banate hain. Iske liye tool chahiye force × distance (mechanics se, Conservation of energy (mechanics)) — choose isliye kiya kyunki work aise hi define hota hai aur koi simpler cheez "energy from pushing" capture nahi karti.

9. $d$ aur $\Delta$ — "ek tiny change" vs "total change"

Topic ko yeh kyun chahiye: work $W=\int PdV$ ko slice-by-slice banana padta hai kyunki $P$ vary karta hai, toh tiny $dV$ chahiye. Final answers, though, finite $\Delta U$ hain, isliye dono notations chahiye. $dU=dQ-dW$ slice-form hai; $\Delta U=Q-W$ summed-up form hai.

10. Sign convention — $dU=dQ-dW$ mein $-$ kyun

Har case ek rule se cover hota hai: $dV$ ka sign dekho. Expansion $\Rightarrow dV>0\Rightarrow W>0$; compression $\Rightarrow dV<0\Rightarrow W<0$; volume change nahi $\Rightarrow dV=0\Rightarrow W=0$.

Prerequisite map

Equipment checklist

Khud test karo — right side chhupao.

Connections

• Parent topic
• Internal energy and degrees of freedom
• Work done in thermodynamic processes (PV diagrams)
• Isothermal, adiabatic, isobaric, isochoric processes
• Heat capacities Cp and Cv
• Conservation of energy (mechanics)
• Second law of thermodynamics