Question bank — Temperature — thermal equilibrium, thermometers, scales

False — energy is baat par bhi depend karti hai ki kitna stuff hai; 20 °C pe ek badi lake, 500 °C pe ek hot needle se bahut zyada thermal energy hold karti hai. Temperature intensive hai, energy extensive hai.

True — equal temperature matlab wo thermal equilibrium mein hain, isliye net heat flow zero hai (dekho Zeroth Law of Thermodynamics).

False — scales ke zeros alag hain. 20 °C se 40 °C jaana gas ko 293 K se 313 K le jaata hai, double ke kahin kareeb nahi, isliye "doubling" sirf Kelvin scale pe meaningful hai.

True — Celsius aur Kelvin degrees same size ke hain (dono pe ice aur steam ke beech 100 divisions); +273.15 offset kisi bhi difference ke liye cancel ho jaata hai.

False — bahar dono air temperature pe hote hain; metal sirf tumhare haath se heat zyada teezi se conduct karti hai, isliye touch conductivity report karta hai, temperature nahi.

True — $P$ versus $t_C$ ki straight line $P=0$ pe $-273.15$ °C par hit karti hai, aur kyunki ideal gas ka pressure negative nahi ho sakta, woh extrapolated crossing hard floor $0$ K mark karti hai.

False — yeh tumhare saath equilibrium reach karne ke baad apna khud ka temperature measure karta hai; Zeroth Law hi hai jo humein phir yeh claim karne deta hai ki woh reading tumhara temperature bhi hai.

False — alag liquids thodi non-linearly expand karte hain aur fixed points ke beech disagree karte hain; sirf dilute (ideal) gases agree karte hain, isliye gas thermometer absolute scale define karta hai.

$+32$ ek origin shift hai, sirf absolute readings ke liye valid hai, differences ke liye nahi. Ek change convert hota hai $\Delta t_F=\frac{9}{5}(15)=27$ °F.

Yeh sirf ek absolute scale deta hai jab property $X$ sachchi mein $T=0$ par zero jaaye; ek mercury column ka absolute zero par finite length hoti hai, isliye yeh proportional form properly gas pressure ya volume ke liye reserved hai, jo wahaan vanish karte hain.

Zeroth Law iska ulta kehta hai — $A$ aur $B$ already ek doosre ke saath equilibrium mein hain, isliye unke beech koi net heat flow nahi hoga.

Linear law $T=aX+b$ mein do unknowns hain; ek point slope aur intercept dono fix nahi kar sakta. Single-fixed-point SI definition sirf isliye kaam karti hai kyunki yeh intercept bhi decree se zero par fix kar deta hai ($T\to 0$ as $X\to 0$).

Origin shift drop kar di gayi; tumhe 32 add karna padega, jo deta hai $98.6$ °F. +32 skip karna ek interval ko actual reading se confuse karta hai.

Classically motion ruk jaati hai, lekin quantum mechanics ek residual zero-point energy chhodti hai; absolute zero minimum energy ki state hai, literally zero energy nahi (link to Kinetic Theory of Gases).

Kyunki saare dilute gases low pressure par universally behave karte hain aur fixed points ke beech agree karte hain, jabki alag liquids non-linearly expand karte hain aur disagree karte hain, isliye gas thermometer substance-choice ambiguity hatata hai.

Yeh guarantee karta hai ki thermal equilibrium transitive hai, isliye saare mutually-equilibrated systems ek consistent number share karte hain; transitivity ke bina, "kisi object ka temperature" well-defined property nahi hoti.

Socho thermometer par ruler banana: ek akela mark tumhe spacing ke baare mein kuch nahi batata, lekin do marks tumhe gap ko equal steps mein kaatne dete hain aur unhe bahar extend karne dete hain — yahi exactly "linear" ka matlab hai, poori taraf ek fixed step size. Yeh sabse simple, most reproducible ruler hai jo tum bana sakte ho, aur koi bhi smoothly-rising property $T$ mein linear defined ki ja sakti hai; price yeh hai ki phir alag substances marks ke beech thoda disagree karti hain.

$P$-versus-$t_C$ figure mein extrapolated line dekho: yeh $-273.15$ °C par zero pressure reach karti hai, aur ideal gas negative pressure se push nahi kar sakti, isliye koi lower state nahi hai — yeh ek sachcha floor hai, koi arbitrary scale origin nahi jo negative dip kar sake.

Transfer ki gayi heat internal energy content par depend karti hai, temperature par nahi; pool ki enormous mass bahut zyada thermal energy carry karti hai apne lower temperature ke bawajood (dekho Heat and Internal Energy).

Do scales alag slopes wali straight lines hain, isliye wo sirf ek baar mil sakti hain. Readings equal set karte hue, $x=\frac{9}{5}x+32$, hum $\frac{9}{5}x$ cross karte hain: $x-\frac{9}{5}x=32$, yaani $-\frac{4}{5}x=32$, toh $x=-\frac{5}{4}\times 32=-40$. Geometrically yeh woh single point hai jahan C-line aur F-line cross karti hain (neeche C-vs-F figure dekho).

$0$ K — proportional definition $T=T_{\text{tr}}P/P_{\text{tr}}$ force karti hai $T=0$ at $P=0$, jo absolute zero hai aur real gas ke liye physically unreachable hai.

Unhone thermal equilibrium reach kar liya hai, isliye unka temperature ab equal hai aur unke beech koi net heat flow nahi hai — lekin yeh settled state describe karta hai, poori history nahi; heat pehle flow hui hogi jab tak cheezein badalna band nahi hui.

Nahi — thermal equilibrium sirf thermal contact ke liye define hota hai (heat pass ho sakti hai, lekin koi work ya matter exchange nahi); unhe allow karna doosre imbalances introduce karega.

Nahi — kisi change ke liye $\Delta T=\Delta t_C$ exactly, kyunki offset kisi bhi difference mein cancel ho jaata hai; +273.15 sirf absolute reading convert karne ke liye lagta hai.

Koi finite nahi — ye har jagah constant 273.15 se differ karte hain, isliye unki straight lines parallel hain aur kabhi cross nahi karti (C aur F se alag, jinke alag slopes unhe $-40$ par milne dete hain).

Ideal gas ke liye yeh holds — ek gas sirf push kar sakti hai. Lekin condensed phases (capillary mein stretched liquid, tall trees mein sap) metastable negative-pressure states mein ho sakti hain jahan wo tension mein hoti hain; yeh ek real, subtle effect hai aur absolute zero define karne ke liye use ki gayi ideal-gas extrapolation ko affect nahi karta.