A gas at $10^{0} C$ temperature and $1.013 \times 10^{5} P a$ pressure is compressed adiabatically to half of its volume. If the ratio of specific heats of the gas 1.4, what is its final temperature

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$93^{0} C$

$146^{0} C$

${100.4}^{0} C$

$123^{0} C$

answer is A.

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Detailed Solution

$\frac{T_{1}}{T_{2}} = {(\frac{V_{2}}{V_{1}})}^{r - 1}$

$\Rightarrow T_{2} = T_{1} \frac{V_{1}^{γ - 1}}{V_{2}^{γ - 1}} = (10 + 273) {(\frac{V_{1}}{V_{2}})}^{γ - 1} = (283) (2)^{1.4 - 1} T_{2} = 373.56 K or T_{2} = 373.56 - 273 T_{2} = {100.56}^{\circ} C$

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