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Question

An ideal gas at a pressure of $$1$$ atmosphere and temperature of $$27^{o}C$$ is compressed adiabatically until its pressure becomes $$8$$ times the initial pressure, then the final temperature is
($$\gamma =3/2$$)


A
6270 C
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B
5270 C
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C
4270 C
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D
3270 C
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Solution

The correct option is D $$327^{0}\ C$$
In an adiabatic process, pressure and temperature are related as
$$\displaystyle PT^{\dfrac {\gamma }{\gamma -1}}=$$constant
$$\displaystyle \left (\dfrac {P_1}{P_2}\right )^{1-\gamma }=\left (\dfrac {T_2}{T_1}\right )^{\gamma }$$
$$\displaystyle \left (\dfrac {1}{8}\right )^{1-1.5}=\left (\dfrac {T_2}{300}\right )^{1.5}$$
$$\displaystyle T_2=300\times {8}^{0.5/1.5}=300(2)=600K=327^o C$$
Option D.

Physics

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