Temperature — thermal equilibrium, thermometers, scales

1.7.1 · Physics › Thermodynamics

Temperature ki zaroorat kyun hai?

Kaunsa problem solve kar rahe hain? Humare senses jhooth bolte hain. Thandi subah mein ek metal doorknob aur ek wooden door ko touch karo — metal zyada thanda lagta hai, jabki dono same temperature par hain. Metal sirf tumhare haath se heat zyada tezi se conduct kar leta hai. Toh "feeling se hot/cold" koi physical quantity nahi ho sakti.

Kyun chahiye ek objective definition: physics ko ek aisa number chahiye jo (a) un do systems ke liye same ho jo heat exchange band kar chuke hain, aur (b) yeh bataye ki heat kis direction mein flow karti agar woh nahi hote.

Zeroth Law — logical foundation

HOW this creates temperature: Equilibrium ek equivalence relation hai (reflexive, symmetric, transitive). Jo bhi systems aapas mein thermal equilibrium mein hain woh ek class banate hain, aur hum ek number — temperature — us class se attach karte hain. Thermometer ( $C$ ) sirf humara standard reference system hai.

Thermometer actually kaise kaam karta hai

One-fixed-point modern definition (SI)

2019/Kelvin scale ke baad se, hum ek single fixed point par anchor karte hain aur slope definition se fix hota hai: $T = T_{tr} \frac{X}{X _{tr}}, T_{tr} = 273.16 K (triple point of water)$ Yeh force karta hai ki $T \to 0$ jab $X \to 0$ , yaani ek absolute zero.

Figure — Temperature — thermal equilibrium, thermometers, scales

Temperature scales — aur conversions, derived

Hum do fixed points use karte hain: melting ice aur boiling water (1 atm par).

Scale	Ice point	Steam point	Divisions
Celsius $t_{C}$	$0$	$100$	$100$
Fahrenheit $t_{F}$	$32$	$212$	$180$
Kelvin $T$	$273.15$	$373.15$	$100$

Gas thermometer aur absolute zero

Worked Examples

Common Mistakes (Steel-manned)

Recall Feynman: ek 12-saal ke bachche ko explain karo

Socho do cups paani, ek hot, ek cold, ek metal spoon se jude hue. Heat hot cup se cold mein spoon ke through chhupta hai jab tak dono "same warm" nahi lagte — phir ruk jaata hai. Woh "same warm" number temperature hai. Thermometer sirf ek tiny cheez hai (jaise mercury ki ek thread) jo garam hone par lamba hota hai; hum iske upar do jaane-maane points — ice melting aur water boiling — mark karke aur gap ko equal steps mein divide karke ek ruler banate hain. Zeroth Law woh promise hai ki agar thermometer tumhari soup se match kare aur tumhari chai se match kare, toh tumhari soup aur chai bhi aapas mein match karti hain. Aur agar tum ek gas ko neeche aur neeche cool karo, iska push (pressure) $- 273.15$ °C par zero ki taraf girta hai — tum zero se kam push nahi kar sakte, toh yahi sabse thanda koi bhi cheez ho sakti hai.

Flashcards

Net heat flow ki direction kaunsi single quantity determine karti hai?

Temperature (heat hot → cold flow karti hai jab tak equal temperatures nahi ho jaatein).

Thermal equilibrium define karo.

Woh state jahan thermal contact mein do systems koi net heat exchange nahi karte aur unke macroscopic properties change hona band ho jaate hain.

Zeroth Law of Thermodynamics batao.

Agar A, C ke saath thermal equilibrium mein hai aur B, C ke saath equilibrium mein hai, toh A, B ke saath equilibrium mein hai.

Zeroth Law thermometers ko kyun justify karta hai?

Yeh "...ke saath equilibrium mein" ko transitive banata hai, toh ek thermometer (C) jo do bodies se agree kare guarantee karta hai ki woh same temperature share karte hain; temperature ek well-defined property ban jaati hai.

Thermometric property kya hai? 3 do.

Ek property jo hotness ke saath reproducibly vary kare — jaise mercury column length, gas pressure (const. V), electrical resistance.

Celsius ko Fahrenheit mein convert karo.

t_{F} = \frac{9}{5} t_{C} + 32

Celsius ko Kelvin mein convert karo.

T = t_{C} + 273.15

Celsius aur Fahrenheit kis temperature par coincide karte hain?

- 40°

(−40 °C = −40 °F).

Temperature ki ek change ke liye, ΔT, Δt_C, Δt_F ko relate karo.

Δ T = Δ t_{C}

aur

Δ t_{F} = \frac{9}{5} Δ t_{C}

(offsets cancel ho jaate hain).

Constant-volume gas thermometer standard kyun hai?

Sabhi dilute (ideal) gases low pressure par identically behave karte hain, toh woh temperature par agree karte hain, alag liquids ke unlike.

Gas thermometer se absolute zero kaise derive hota hai?

P = P_{0} (1 + α t_{C})

P = 0

tak extrapolate karo, deta hai

t_{C} = - 1/ α = - 273.15° C = 0

Single-fixed-point Kelvin definition formula.

T = T_{t r} \frac{X}{X _{t r}}

jahan

T_{t r} = 273.16

K (triple point of water).

Temperature absolute zero se neeche kyun nahi ja sakta?

Yeh zero gas pressure se correspond karta hai; pressure negative nahi ho sakta, toh 0 K ek hard lower limit hai.

Connections

Heat and Internal Energy — temperature vs heat (intensive vs energy in transit)
Zeroth Law of Thermodynamics — temperature measure karne ka formal basis
Ideal Gas Law — $P V = n R T$ gas thermometer aur absolute scale ko underlie karta hai
Thermal Expansion — mercury/liquid thermometers ka basis
First Law of Thermodynamics — jahan heat $Q$ aur energy bookkeeping start hoti hai
Kinetic Theory of Gases — microscopic meaning: $T \propto$ mean molecular KE