MHT CET · Physics · Kinetic Theory of Gases
The r.m.s. speed of gas at temperature \(T\) is 2 times the r.m.s speed at \(320 \mathrm{~K}\). The value of the Temperature \(T\) is
- A \(1280 \mathrm{~K}\)
- B \(960 \mathrm{~K}\)
- C \(640 \mathrm{~K}\)
- D \(2560 \mathrm{~K}\)
Answer & Solution
Correct Answer
(A) \(1280 \mathrm{~K}\)
Step-by-step Solution
Detailed explanation
According to the kinetic theory of gases the Kinetic energy of a molecule is proportional to the temperature.
\(\begin{aligned} & \frac{K_1}{K_2}=\frac{T_1}{T_2}=\left(\frac{v_1}{v_2}\right)^2 \\ & \Rightarrow \frac{T_1}{320 \mathrm{~K}}=\left(\frac{2}{1}\right)^2 \\ & \Rightarrow T_1=1280 \mathrm{~K}\end{aligned}\)
\(\begin{aligned} & \frac{K_1}{K_2}=\frac{T_1}{T_2}=\left(\frac{v_1}{v_2}\right)^2 \\ & \Rightarrow \frac{T_1}{320 \mathrm{~K}}=\left(\frac{2}{1}\right)^2 \\ & \Rightarrow T_1=1280 \mathrm{~K}\end{aligned}\)
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