Question

19 2 bulbs X and Y are filled with an ideal gas and connected by a capillary tube. The volume of bulb X is three times that of bulb Y. The number of gas molecules in X and Y are 2N and N respectively. If the temperature of the gas in Y is 300 K, what is the temperature of the gas in X
150 K
200 K
450 K
600 K

Answer 1

Answer on Question #51932-Physics-Field Theory

19 2 bulbs X and Y are filled with an ideal gas and connected by a capillary tube. The volume of bulb X is three times that of bulb Y. The number of gas molecules in X and Y are 2N and N respectively. If the temperature of the gas in Y is 300 K, what is the temperature of the gas in X

150 K

200 K

450 K

600 K

Solution

For equilibrium should be

$$P _ {X} = P _ {Y},$$

where $P_{X}$ is pressure of gas in bulb X, $P_{Y}$ is pressure of gas in bulb Y.

The pressure is given by the formula

$$P = \frac {N}{V} k T.$$

Thus,

$$\frac {2 N}{3 V} k T _ {X} = \frac {N}{V} k T _ {Y}.$$

So, the temperature of the gas in X is

$$T _ {X} = \frac {3}{2} T _ {Y} = \frac {3}{2} 300 \mathrm {K} = 450 \mathrm {K}.$$

Answer: 450 K.

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