Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume ? (R = 8.3 J/mol K)

When M₁ gram of ice at –10^oC (specific heat = 0.5 cal g^{–1 o}C^–1 ) is added to M₂ gram of water at 50C, finally no ice is left and the water is at 0°C. The value of latent heat of ice, in cal g^–1 is :

At 40^o C, a brass wire of 1 mm radius is hung from the ceiling. A small mass, M is hung from the free end of the wire. When the wire is cooled down from 40^oC to 20^oC it regains its original length of 0.2 m. The value of M is close to : (Coefficient of linear expansion and Young’s modulus of brass are 10^–5 /^oC and 10¹¹ N/m ² , respectively; g= 10 ms^–2 )

One mole of ideal gas passes through a process where pressure and volume obey the relation $$P = {P_0}\left[ {1 - {1 \over 2}{{\left( {{{{V_0}} \over V}} \right)}^2}} \right]$$. Here P₀ and V₀ are constants. Calculate the change in the temperature of the gas if its volume changes form V₀ to 2V₀