Question

0.1 mole of a gas at 200 k is mixed with 0.5 mole of same gas at 400K. if final temperature is equal to 10T_0 then find the value of T_0? ​

Answer 1

Given : 0.1 mol of a gas at 200K is mixed with 0.5 mol of same gas at 400K.

To find : if the final temperature is equal to 10T₀ then we have to find the value of T₀.

solution : let final temperature is T,

we know heat flows from higher temperature to lower temperature.

so, heat lost by 0.5 mol of a gas = heat gained by 0.1 mol of the gas

⇒0.5 × S × (400 - T) = 0.1 × S × (T - 200K)

⇒5(400 - T) = T - 200

⇒2000 - 5T = T - 200

⇒6T = 2200

⇒T = 1100/3 ≈ 367 K

given The final temperature is 10T₀

so, 10T₀ = 367

⇒T₀ = 36.7

Therefore the value of T₀ is 36.7