Physics Thermodynamics

3C (Graphite) + 4H₂ (g) -> C₃H₈ (g)

$\Delta H_f\left(C_3{H}_8\right)=\left[3*\Delta H_{comb}\left(C\right)\right]+\left[4*\Delta H_{comb}\left(H_2\right)\right]-\left[\Delta H_{comb}\left(C_3{H}_8\right)\right]$        

= -10.3.7 kJ/mole

For adiabatic process – PV^Y = const

$T_1{V_1}^{Y-1}=T_2{V}_2^{Y-1}$

$\frac{T_2}{T_1}={\left(\frac{v_1}{v_2}\right)}^{Y-1}={\left(\frac{d_2}{d_1}\right)}^{Y-1}={\left(32\right)}^{\left(\frac{7}{5}-1\right)}={\left(32\right)}^{2/5}$

$={\left(2\right)}^2=4$

$Q_1=\underset{water}{20°C}\to 100°steam$

$Q_1=mc\Delta T+mL$

$=m\left[c\Delta T+L\right]$

$=31000=31*10^{3}cal$

$Q_2=\frac{293}{373}*31*10^3$

$=24.35*10^{3}cal$

 $\frac{dT}{dt}=-k\left(T-T_0\right)$

$\frac{dT}{\left(T-T_0\right)}=-kdt$

$\Rightarrow k=-\frac{1}{6}\mathcal{l}n\left(\frac{2}{3}\right)$ - (1)

Now $\frac{dT}{dt}=-k\left(T-T_0\right)$

t = 10.257

t₂ = 6 + 10.257 = 16.257 minutes

16.25 and or 16

$Q=\Delta \upsilon +w\Rightarrow nC\Delta T=n{C}_v\Delta T=\frac{nC\Delta T}{4}=\frac{3}{4}nC\Delta T=n{C}_v\Delta T$

$C=\frac{4}{3}{C}_v=\frac{4}{3}*\frac{3}{2}R=2R$

Heating energy $=\frac{1}{4}th$ energy of the hammer

$=\frac{1}{4}*\frac{1}{2}m{v}^2$

$=\frac{1}{4}*\frac{1}{2}*1.5*60*60$

$=\frac{15*6*60}{4*2}$

= 675 J

$\Delta T=\frac{675}{42}=16.07°C$

0.25 = 1 - $\frac{T_2}{T_1}$ $\frac{{}_{}}{{}_{}}$

0.25 = 1 - $\frac{\left(27+273\right)}{T_1}\Rightarrow \frac{300}{T_1}=1-0.25$ $\frac{}{{}_{}}\frac{}{{}_{}}$

$\Rightarrow \frac{300}{T_1}=0.75$

$T_1=\frac{300*100}{75}$

T1 = 400 k

Now, efficiency increases by 100%

${\eta }_2=100\mathrm{\%}{\eta }_1+{\eta }_1$

$=2{\eta }_1$

= 0.25 * 2

= 0.50

0.50 = 1 - $\frac{T_2\text{'}}{T_1}$ $\frac{{}_{}}{{}_{}}$

$\Rightarrow \frac{T_2\text{'}}{T_1}=0.50$

$T_1\text{'}=\frac{300}{0.5}$

$T_1\text{'}=600k$

$$ $T_1\text{'}-T_1=$  (600 – 400) = 200 k or 200° C

One of the most important Mechanical Engineering subjects is Thermodynamics, which deals with the concepts of heat energy and temperature, along with its conversion between different forms. You would come across a variety of books that will give you a basic understanding of the concept, but here are a few book suggestions for Mechanical Engineering freshers to grasp the basics of thermodynamics quickly

• Basic and Applied Thermodynamics by P. K. Nag
• Engineering Thermodynamics by S. K. Som & G. Biswas
• The Laws of Thermodynamics: A Very Short Introduction by Peter Atkins

In GATE XE (Engineering Sciences), Thermodynamics is one of the optional sections (XE-E), but admissions for M.Tech are usually branch-specific (like Mechanical, Thermal, Energy Engineering).