The temperature of a gas is – 78°C and the average translational kinetic energy of its molecules is K. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2K is

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Solution

Q.
The temperature of a gas is – 78°C and the average translational kinetic energy of its molecules is K. The temperature at which the average translational kinetic energy of the molecules of the same gas becomes 2K is [2024]

1 – 39°C

2 117°C

3 127°C

4 – 78°C

Ans.
(2)

Average translational kinetic energy

   $E = \frac{3}{2} K_{B} T$

At – 78°C = 273 – 78 = 195 K

$K = \frac{3}{2} K_{B} \times (195 K)$ ...(i)

  Now when kinetic energy becomes 2K, the temperature is T K.

   $∴$    $2 K = \frac{3}{2} K_{B} \times (T K)$ ...(ii)

From equations (i) and (ii)

   $\frac{K}{2 K} = \frac{195}{T}$

   $\Rightarrow$ T = 390 K

$∴$ in °C, 390 – 273 = 117°C

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