JEE Main 2011 — Thermodynamics

Three perfect gases at absolute temperatures $T_1, T_2$ and $T_3$ are mixed. The masses of molecules are $m_1$, $m_2$ and $m_3$ and the number of molecules are $n_1, n_2$ and $n_3$ respectively. Assuming no loss of energy, the final temperature of the mixture is :

$100 \mathrm{~g}$ of water is heated from $30^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is $4148 \mathrm{~J} / \mathrm{kg} / \mathrm{K}$ ):

A thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma$. It is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by :