Question

$1m{m}^3$ of a gas is compressed at 1 atmospheric pressure and from temperature $27^{\circ }C$ to $627^{\circ }C$. What is the final pressure under adiabatic condition $(\gamma$ for the gas $=1.5)$ ?

• A. $27\times 10^{5}N/m^2$
• B. $80\times 10^{5}N/m^2$
• C. $36\times 10^{5}N/m^2$
• D. $56\times 10^{5}N/m^2$

Answer 1

Answer: (A)

Here, $P=10^{5}N/m^2,T_1=27+273=300K$
$T_2=627+273=900K$ and $\gamma =1.5$
For adiabatic change, $\frac{T_{\gamma }}{p^{\gamma -1}}=$ constant
${\left(\frac{p_2}{p_1}\right)}^{1/2}={\left(\frac{T_2}{T_1}\right)}^{3/2}$
$\Rightarrow {\left(\frac{p_2}{105}\right)}^{1/2}={\left(\frac{900}{300}\right)}^{3/2}$
$\Rightarrow p_2=27\times 10^{5}N/m^2$