A) \[10\,K\]
B) \[{{10}^{2}}K\]
C) \[{{10}^{3}}\,K\]
D) \[{{10}^{4}}\,K\]
Correct Answer: D
Solution :
The root mean square velocity of gas \[{{v}_{rms}}=\sqrt{\frac{3KT}{m}}\] ?. (i) Escape velocity of gas molecules \[{{v}_{es}}=\sqrt{2g{{R}_{e}}}\] ? (ii) At the root mean square velocity of gas, molecule must be equal to the escape velocity. From Eq. (i) and (ii), we get \[\sqrt{\frac{3KT}{m}}=\sqrt{2g{{R}_{e}}}\] \[T=\frac{2g{{R}_{e}}m}{3K}\] \[T=\frac{2\times 9.8\times 6.4\times {{10}^{6}}\times 0.34\times {{10}^{-26}}}{3(1.38\times {{10}^{-23}})}={{10}^{4}}K\]
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