Question

An ideal Braton cycle, operatingg between the pressure limits of (1\) bar and $6$ bar, has minimum and maximum temperatures of $300K$ and $1500K$. The ratio of specific heats of the workingg fluids is $1.4$. The approximate final temperature in Kelvin at the end of the compresssion and expansion processes are respectively

• A. $500$ and $900$
• B. $900$ and $500$
• C. $500$ and $5400$
• D. $900$ and $900$

Answer 1

The correct option is A $500$ and $900$



Given data:
$p_1=1bar;p_2=6bar$
$T_1=300K;T_3=1500K$
For process $1-2$
$\frac{T_2}{T_1}={\left(\frac{p_2}{p_1}\right)}^{\frac{\gamma -1}{\gamma }}$
$\frac{T_2}{300}={\left(\frac{6}{1}\right)}^{\frac{1.4-1}{1.666}}=(6{)}^{0.285}=1.666$
or T_2=300\time 1.666
$=499.8K=500K$
For process $3-4$
$\frac{T_3}{T_4}={\left(\frac{p_3}{p_4}\right)}^{\frac{\gamma -1}{\gamma }}={\left(\frac{p_2}{p_1}\right)}^{\frac{\gamma -1}{\gamma }}$
$\because ,p_3=p_2,p_4=p_1$
$\frac{1500}{T_4}=(6{)}^{\frac{1.4-1}{1.4}}=(6{)}^{0.285}=1.666$
or $T_4=\frac{1500}{1.666}=900.36K=900K$