Question

Inside the engine of an automobile, the cylinder compresses the air from approximately standard temperature and pressure to one-twentieth of the original volume and a pressure of $50\, atm$. What is the temperature of the compressed air?

• A. 500 K
• B. 682 K
• C. 550 K
• D. 1000 K
• E. 200 K

Answer 1

Answer: (B)

As, we know the standard temperature and pressure are $273\, K$ and 1 atm, respectively.
So, from ideal gas equation
$p V=n R T$
Ratio $\frac{p_{1} V_{1}}{p_{2} V_{2}}=\frac{T_{1}}{T_{2}}$
Given, $p_{1}=1$ atm, $p_{2}=50$ atm, $V_{1}=V$
$V_{2}=\frac{V}{20} \text { and } T_{1}=273\, K$
$\Rightarrow \frac{1 \times V}{50 \times \frac{V}{20}}=\frac{273}{T_{2}}$
$\Rightarrow T_{2}=682\, K$