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Two thermally insulated vessel 1 and 2 a...

Two thermally insulated vessel 1 and 2 are filled with air at temperature `(T_1T_2), volume (V_1V_2)` and pressure `(P_1P_2)` respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

A

`T_1 + T_2`

B

`(T_1 + T_2)//2`

C

`(T_1 T_2(V_1 + V_2))/(p_1 V_1 T_2 + p_2 V_2 T_1)`.

D

`(T_1 T_2(p_1V_1 + p_2 V_2))/(p_1 V_1 T_2 + p_2 V_2 T_1)`.

Text Solution

Verified by Experts

The correct Answer is:
C
`(n_1 + n_2)_i = (n_1 + n_2)_f`
`:. (p_1 V_1)/(R T_1) + (p_2 V_2)/(R T_2)= ((V _1 + V_2))/(R T)`
Solving, we get `T = (T_1 T_2 p(V_1 + V_2))/(p_1 V_1 T_2 + p_2 V_2 T_1)`.
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Knowledge Check

  • Two thermally insulated vessel 1 and 2 are filled with air temperature (T_(1),T_(2)) , volume (V_(1),V_(2)) and pressure (P_(1),P_(2)) respectively. If the valve joining the two vessels is opened, the temperature inside the vessel at equilibrium will be

    A
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    B
    `((T_(1)+T_(2)))/(2)`
    C
    `(T_(1)T_(2)(P_(1)V_(1)+P_(2)V_(2)))/(P_(1)V_(1)T_(2)+P_(2)V_(2)T_(1))`
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    `(T_(1)T_(2)(P_(1)V_(1)+P_(2)V_(2)))/(P_(1)V_(1)T_(1)+P_(2)V_(2)T_(2))`

  • Two identical vessels contain the same gas at pressure P_(1) and P_(2) at absolute temperature T_(1) and T_(2) , respectively. On joining the vessels with a small tube as shown in the figure. The gas reaches a common temperature T and a common pressure P. Determine the ratio P//T

    A
    `[(P_(1) T_(1) + P_(2) T_(2))/(T_(1) T_(2))]`
    B
    `(1)/(2)[(P_(1) T_(1) + P_(2) T_(2))/(T_(1) T_(2))]`
    C
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    A
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    C
    `(P_(1)T_(2) + P_(2) T_(2))/((T_(1) + T_(1))^(2))`
    D
    `(P_(1))/(2T_(1)) + (P_(2))/(2T_(2))`

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