1.7.10 · D5 · HinglishThermodynamics
Question bank — Internal energy of ideal gas U = (f - 2)nRT
1.7.10 · D5· Physics › Thermodynamics › Internal energy of ideal gas U = (f - 2)nRT
True ya false — justify karo
Har statement ya toh true hai ya false. Batao kaun sa, aur — yahi poora point hai — ek line ki real physics mein kyon batao.
Ek ideal gas ki internal energy uske volume par depend karti hai.
False. Ideal gas mein koi intermolecular forces nahi hote, isliye molecules ke beech ki spacing mein koi potential energy nahi chupi hoti — pure kinetic energy hai aur kinetic energy sirf track karti hai, jo deta hai .
Agar tum constant temperature par ek ideal gas ka volume double kar do, toh uski internal energy double ho jaati hai.
False. Constant ka matlab hai constant molecular speeds; molecules ke paas bas ghoomne ke liye zyada jagah ho jaati hai. chahe ke saath kuch bhi ho.
Same temperature par do gas samples ki internal energy hamesha same hoti hai.
False. moles ki sankhya aur degrees of freedom ke saath bhi scale karta hai. Same lekin alag ya alag molecular structure alag deta hai.
Gas ko heat karna hamesha uski internal energy badhata hai.
False. par depend karta hai, heat par nahi. Isothermal expansion mein tum heat supply karte ho phir bhi , isliye — heat work ke roop mein nikalta hai (dekho First law of thermodynamics).
Ek ideal gas ke liye, same do temperatures ko connect karne wale kisi bhi process ke liye same hota hai.
True. sirf ka ek state function hai, isliye sirf endpoints par depend karta hai, unke beech li gayi path par nahi.
Equipartition rule per molecule apply hota hai, per mole nahi.
True. Har quadratic degree of freedom per molecule carry karta hai; molecules se multiply karke aur use karke per-mole form milta hai (dekho Equipartition theorem).
Same par ek monatomic aur ek diatomic gas ki average translational kinetic energy per molecule same hoti hai.
True. Translational KE per molecule dono ke liye hai — ye sirf par depend karta hai. Diatomic ki extra energy uske 2 rotational modes mein rehti hai, faster translation mein nahi.
Internal energy mein container ki kinetic energy shamil hai jo table par slide kar raha ho.
False. strictly microscopic random energy hai; poore container ki ordered bulk motion external kinetic energy hai, jo deliberately se bahar rakhi jaati hai.
Error dhundho
Har line mein ek galat statement ya reasoning step hai. Dhundho aur theek karo.
"Sabhi gases ke liye, kyunki translation mein 3 degrees of freedom hain."
Error hai ko universally use karna. Ye sirf monatomic ke liye hai. Diatomic aur polyatomic gases rotational (aur high par vibrational) modes add karte hain, isliye 5, 6, ya zyada ho sakta hai — .
"Isothermal expansion mein gas kaam karta hai, isliye uski internal energy zaroor giregi."
Ideal gas ke liye sirf par depend karta hai, aur constant hai, isliye . Kiya gaya kaam absorbed heat se pay hota hai (), internal energy mein se nahi.
"Maine heat add ki, isliye badh gayi."
Ye sirf constant volume par sach hai jahan . Generally first law kehta hai , isliye us heat ka kuch hissa work ban sakta hai — , se kam ho sakta hai.
"Ek diatomic molecule 3 axes ke around ghoomti hai, isliye uske 3 rotational degrees of freedom hain."
Bond axis ke around rotation ka negligible moment of inertia hota hai (mass us line par baith jaata hai), isliye woh mode freeze out ho jaata hai. Sirf 2 perpendicular axes count karte hain, jo deta hai .
"Kyunki sirf par depend karta hai, aur same hai, toh same par ek ideal gas aur ek real gas ki internal energy equal hogi."
" only" statement ek ideal-gas result hai. Ek real gas mein intermolecular forces hote hain, isliye potential energy jo volume ke saath vary karti hai, toh uska par bhi depend karta hai.
"Equipartition har molecule ko exactly energy deta hai."
Ye per molecule average energy deta hai. Individual molecules ki speeds mein wide spread hoti hai; sirf ensemble average ke barabar hota hai.
"Nitrogen gas process ke liye nikaalने ke liye mujhe jaanna hoga ki woh isobaric tha ya isochoric."
Nahi jaanna — ko sirf chahiye. Path aur ke liye alag-alag matter karta hai, lekin ke liye nahi (dekho Molar specific heats Cv and Cp).
Why questions
"Why" ka jawab mechanism se do, restatement se nahi.
Ideal gas ki internal energy temperature par kyun depend karti hai lekin pressure par nahi?
Temperature average molecular kinetic energy ka direct measure hai, jo ideal gas ke liye hai hi internal energy; pressure sirf itna hai ki molecules walls se kitni baar takraate hain aur koi alag stored energy carry nahi karta kyunki koi intermolecular forces nahi hain.
Hum energy-per-molecule ko se kyun multiply karte hain aur phir ko se swap karte hain?
se multiply karna per-molecule average ko poore sample ki total energy mein badalta hai; swap karna microscopic molecule count ko macroscopic, measurable quantity of moles mein convert karta hai (dekho Ideal gas law).
Har degree of freedom ko exactly kyun milta hai, zyada nahi?
Equipartition statistical mechanics se aata hai: koi bhi energy term jo kisi coordinate ya velocity mein quadratic hai, independently same average par thermalize hoti hai, kyunki energy sabhi independent quadratic modes mein democratically share hoti hai.
ko "state function" kyun kehte hain?
Kyunki uski value poori tarah current state se fix hoti hai (ideal gas ke liye, aur se) — use yaad nahi ki gas wahan kaise pahunchi, isliye do states ke beech path-independent hai.
Rotational degrees of freedom add karne se gas ko heat karna mushkil kyun ho jaata hai (zyada heat capacity)?
Supply ki gayi energy zyada modes mein share karni padti hai, isliye ek given input translational (temperature-setting) energy kam badhata hai — har joule ka zyada hissa rotation mein jaata hai, isliye temperature rise ke liye zyada heat chahiye.
Ek diatomic gas bahut kam temperature par monatomic gas ki tarah () kyun behave kar sakti hai?
Rotational modes ko activate hone ke liye minimum quantum of energy chahiye; kam par collisions itne gentle hote hain ki unhe excite nahi kar pate, isliye woh modes "freeze out" ho jaate hain aur sirf 3 translational DOF respond karte hain.
Edge cases
Boundary aur degenerate scenarios — woh jo exams mein chupaaye jaate hain.
Ek ideal gas ki vacuum mein free (Joule) expansion ke liye kya hai?
Zero. Koi heat exchange nahi hoti aur vacuum ke against koi kaam nahi hota, isliye , aur kyunki hai toh temperature bhi unchanged rehta hai.
Absolute zero, par ek ideal gas ka kya hai?
Classically — saari molecular motion ruk gayi hai. (Quantum zero-point energy ek real-gas refinement hai jo ideal model se aage hai.)
Ek cyclic process jo starting state par wapas aata hai, uske liye total kya hai?
Exactly zero, kyunki ek state function hai: same start aur end state matlab same , isliye poore cycle mein regardless of loop ki shape.
Agar ek gas heat ki jaaye lekin saath hi utna hi kaam kare jitna heat supply ki gayi, toh ka kya hoga?
Ye constant rehta hai: . Ye precisely isothermal case hai, jahan saari incoming heat work mein convert ho jaati hai.
Bahut high temperature par diatomic gas ko heat karne par (aur isliye same ke liye ) ka kya hota hai?
Vibrational modes switch on ho jaate hain, 2 aur DOF add karte hain (ek kinetic, ek potential), ko 7 ki taraf le jaate hain, isliye ek baar vibrations activate hone ke baad same ke liye badhta hai.
Monatomic gas ke liye, kya heating se kabhi 3 se zyada ho sakta hai?
Nahi — ek point-like single atom mein koi rotational ya vibrational structure nahi hota jo excite ho sake, isliye sabhi attainable temperatures par 3 rehta hai.
Connections
- Kinetic theory of gases — jahan se per molecule aata hai
- Equipartition theorem — -per-mode rule jinpar ye traps lean karte hain
- First law of thermodynamics — , heat-vs-energy traps ki jaad
- Degrees of freedom — kyun structure aur temperature ke saath badalta hai
- Molar specific heats Cv and Cp — ki path dependence vs ki path independence
- Ideal gas law — conversion