Question 607: Thermodynamics & KTG

Question

A monoatomic ideal gas is compressed adiabatically to $\left(\frac{1}{27}\right)$ of its initial volume. If initial temperature of the gas is ' T ' K and final temperature is ' xT ' K , the value of ' x ' is

Accepted Answer

For an adiabatic process $\mathrm{TV}^{\gamma-1}=$ constant.
$$ \begin{aligned} 	herefore \quad \frac{\mathrm{T}_2}{\mathrm{~T}_1} & =\left(\frac{\mathrm{V}_1}{\mathrm{~V}_2}ight)^{\gamma-1} \ & =\left(\frac{27}{1}ight)^{\frac{5}{3}-1} \ldots\left(ight. given, \left.\mathrm{V}_2=\frac{1}{27} \mathrm{~V}_1ight)\end{aligned} $$
$$ \begin{array}{ll}  & \frac{T_2}{T_1}=(27)^{\frac{2}{3}}=9 \ 	herefore \quad & T_2=9 	imes T_1 \Rightarrow x T_1=9 	imes T_1 \ 	herefore \quad & x=9 \end{array} $$

Answer

7

Answer

9

Answer

11

Answer

13

Thermodynamics & KTG

A monoatomic ideal gas is compressed adiabatically to \left(\frac{1}{27}\right) of its initial volume. If initial temperature of the gas is ' T ' K and final temperature is ' xT ' K , the value of ' x ' is

Choose the correct answer: