Figure shows two rigid vessels A and B, each of volume 200 cm^{3} containing an ideal gas (C_{V} = 12.5 J K^{–1} mol^{–1}). The vessels are connected to a manometer tube containing mercury. The pressure in both the vessels is 75 cm of mercury and the temperature is 300 K.

(a) Find the number of moles of the gas in each vessel.

(b) 5.0 J of heat is supplied to the gas in the vessel A and 10 J to the gas in the vessel B. Assuming no appreciable transfer of heat from A to B calculate the difference in the heights of mercury in the two sides of the manometer. Gas constant R = 8.3 J K^{–1} mol^{–1}.

**Given:**

Gasses in both the vessels are at pressure of 75cm of mercury.

Therefore,

The volume of the vessel is

The temperature of the gas is 300K

(a) For Ideal gasses,

where P,V and T are the pressure, volume and temperature of the gas, n is the number of moles, and R is the gas constant.

⇒

Therefore, number of moles = 0.008

(b) The specific heat of the gas at constant volume is C_{V} = 12.5 J K^{–1} mol^{–1}

Therefore,

Where n is the number of moles, T is the rise in temperature, Q is the heat given.

Therefore, at constant volume, if we supply 5J and 10J heat to the vessels, the rise of temperature will be and

So the change in pressure in the vessels will be governed by

So for the first vessel, Change in pressure

For the second vessel

Therefore, the difference of pressure of the two vessels is

Which is equivalent to of mercury.

Therefore, the height of the mercury in the manometer tube is 12.5cm

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