Question bank — Review of thermodynamics applied to flow — first law for open systems

False — ye ek fixed lump of matter ke liye bilkul sahi hai, aur SFEE isi se derive hoti hai. Ye open systems ke liye sirf inconvenient hai kyunki tab humein flow work ko haath se wapas add karna padta hai; enthalpy wo work hamare liye chhupa deta hai.

False — $pv$ wo work hai jo boundary par kiya jaata hai packet ko ek port ke across push karne ke liye; ye stored internal energy nahi hai. Ye sirf isliye bookkeeping-convenient ban jaata hai kyunki ye hamesha stored $u$ ke saath pair karta hai aur $h$ deta hai.

True — $h_0=h+\frac{1}{2}{V}^2$ constant rehta hai, isliye jab flow accelerate hoti hai ($V\uparrow$) toh static enthalpy $h$ ko girna padta hai taaki sum fixed rahe.

True — gas ke liye, kisi bhi realistic height par $gz$, $h$ aur $\frac{1}{2}{V}^2$ ke muqable mein bahut chota hai, isliye ise neglect karna standard hai; kisi liquid ke liye badi height par ye matter kar sakta hai.

False — sirf tab jab $q=0$, $w_s=0$ aur $\Delta (\frac{1}{2}{V}^2+gz)=0$ ho. Ek turbine $w_s>0$ extract karta hai, ek heater $q$ add karta hai, ek nozzle $h$ ko KE ke liye trade karta hai — in sab mein $h$ change hoti hai.

True — kyunki $h=c_{p}T$ jahan $c_p$ constant hai, $h$ aur $T$ saath-saath move karte hain; $h$ ka girna 곧 $T$ ka girna hai.

False — flow work $pv$ pehle se $h$ ke andar absorb ho chuka hai; sirf shaft work $w_s$ explicitly appear karta hai. $pv$ ko dobara list karna double-counting hai.

True — $q=0$ ke saath balance deta hai $w_s=h_1-h_2$; work gas par kiya jaata hai ($w_s<0$), isliye $h_2>h_1$ aur gas heat addition ke bina bhi garam ho jaati hai.

Internal energy $u$ ki jagah enthalpy $h=u+pv$ hona chahiye; likhne wale ne flow-work terms $p_1{v}_1$ aur $p_2{v}_2$ drop kar diye jo $u$ ko $h$ mein convert karte hain.

$h_2>h_1$ ke saath value $h_1-h_2$ negative hai, isliye $w_s<0$; negative sign hi woh signal hai ki work-out convention ke under work andar supply kiya gaya hai.

Ek adiabatic nozzle mein $h+\frac{1}{2}{V}^2$ constant hai, isliye KE gain karne par enthalpy kharch hoti hai — air actually fast exit par thandi hoti hai, garam nahi.

Nose flow ko rok deta hai, isliye probe (lagbhag) stagnation temperature $T_0=T+V^2/2c_p$ read karta hai, jo $T$ se zyada hota hai — yahi aerodynamic heating hai.

Inlet par andar push karna system par kiya gaya work hai, isliye ye balance mein $-p_1{v}_1$ ki tarah enter karta hai (equivalently ye packet mein energy add karta hai); likhne wale ne sign ulta kar diya.

Ek inlet aur ek outlet wali steady flow mein mass conservation se ${\dot{m}}_{in}={\dot{m}}_{out}$ forced hai (Conservation of mass — continuity equation); narrow pipe velocity change karta hai, mass flow rate nahi.

Kyunki specific volume $v$ wale ek packet ko pressure $p$ par kisi face ke across move karna inevitably $pv$ ka pushing work cost karta hai, aur woh packet apna stored $u$ bhi carry karta hai — kisi bhi port par dono alag nahi hote, isliye nature unhe $h=u+pv$ ke roop mein "pre-bundle" karta hai.

Kyunki $h=u+pv$ define karne se unavoidable flow work absorb ho jaata hai, aur SFEE clean reh jaati hai bina kisi explicit $pv$ terms ke — maths us physics ko mirror karta hai ki flow work hamesha present rehta hai.

Kyunki energy conservation sirf matter ke ek fixed chunk ke liye guaranteed hai; hum ek travelling lump (closed) ko follow karte hain aur sirf baad mein result ko fixed control volume ke liye reinterpret karte hain.

Kyunki perfect gas ke liye $h=c_{p}T$ hai, isliye $h+\frac{1}{2}{V}^2$ conserve karna directly $T$ aur $V^2$ ke beech ek trade ban jaata hai — kinetic energy ka har bit thermal energy se borrow kiya jaata hai.

Convention $w_s$ ko work out leta hai; turbine work out deliver karta hai ($w_s>0$), jabki compressor work consume karta hai, yaani work out negative hai ($w_s<0$).

Ye deta hai $h_1=h_2$ — enthalpy conserve hoti hai chahe pressure sharply drop ho; yahi ek throttling (isenthalpic) process ki defining feature hai.

Ye stagnation enthalpy $h_0$ hi hoti hai, kyunki $h_0=h+\frac{1}{2}{V}^2$ aur velocity term vanish ho jaata hai — flow ki poori energy static enthalpy ke roop mein dikhti hai.

Ye reduce ho jaati hai $h\approx \text{const}$ mein, aur incompressible low-speed limit mein ye Bernoulli's equation ko pressure–velocity trade ke roop mein recover karta hai.

Approximately, haan — fast flow mein "adiabatic" ka matlab hai ki per unit mass meaningful heat exchange ke liye time hi nahi hota, isliye $q\approx 0$ ek achha model hai chahe perfect insulation na ho.

Haan ek adiabatic, no-shaft streamline par total enthalpy conserve hoti hai; single-inlet SFEE ko bas har stream ke $\dot{m}(h+\frac{1}{2}{V}^2)$ alag-alag sum karne mein dhyan rakhna padta hai.

Ye constant rehta hai — kyunki $h_0=c_p{T}_0$ aur $h_0$ conserve hoti hai, stagnation temperature unchanged rehta hai chahe static $T$ aur $V$ swap ho jaayein (Nozzles and diffusers).