Question

Two closed containers of equal volume filled with air at pressure P and temperature T.Both are connected by a narrow tube.if one of the container is maintained at temperature T and other at temperature T' ,then new pressure in the container will be ?

Answer 1

Answer on Question #42747, Physics, Molecular Physics | Thermodynamics

Two closed containers of equal volume filled with air at pressure P and temperature T. Both are connected by a narrow tube. If one of the container is maintained at temperature T and other at temperature T', then new pressure in the container will be?

Solution:

The ideal gas law is

$$\frac {P _ {1} V _ {1}}{T _ {1}} = \frac {P _ {2} V _ {2}}{T _ {2}}$$

The ideal gas law in our case is

$$\frac {P V}{T} + \frac {P V}{T} = \frac {P ^ {\prime} V}{T} + \frac {P ^ {\prime} V}{T ^ {\prime}}$$

Thus,

$$\frac {P (2 V)}{T} = P ^ {\prime} V \left(\frac {1}{T} + \frac {1}{T ^ {\prime}}\right)$$

So,

$$P ^ {\prime} = \frac {2 P}{T} \frac {1}{\left(\frac {1}{T} + \frac {1}{T ^ {\prime}}\right)} = \frac {2 P}{1 + \frac {T}{T ^ {\prime}}}$$

Answer.

$$P ^ {\prime} = \frac {2 P}{1 + \frac {T}{T ^ {\prime}}}$$

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