Answer :

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 CV = 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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