Thermodynamics

A closed vessel contains 0.1 mole of a monatomic ideal gas at 200 K. If 0.05 mole of the same gas at 400 K is added to it, the final equilibrium temperature (in K ) of the gas in the vessel will be close to

Match the Cp/Cv ratio for ideal gases with different type of molecules:
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The specific heat of water = 4200 J kg⁻¹ K⁻¹ and the latent heat of ice = 3.4 * 10⁵ J kg⁻¹. 100 grams of ice at 0°C is placed in 200 g of water at 25°C. The amount of ice that will melt as the temperature of water reaches 0°C is close to (in grams):

If minimum possible work is done by a refrigerator in converting 100 grams of water at $0^{\circ }\mathrm{C}$  to ice, how much heat (in calories) is released to the surroundings at temperature ${27}^{\circ }\mathrm{C}$ (Latent heat of ice $\left.=80\mathrm{C}\mathrm{a}\mathrm{l}/\mathrm{g}\mathrm{r}\mathrm{a}\mathrm{m}\right)$ to the nearest integer?             

Match the $C_p/C_V$ ${}_{}{}_{}$ ratio for ideal gases with different type of molecules:

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To raise the temperature of a certain mass of gas by ${50}^{\circ }\mathrm{C}$ at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by ${100}^{\circ }\mathrm{C}$  at constant volume, 240 calories of heat is released. How many degrees of freedom does each molecule of this gas have (assume gas to be ideal)?

The specific heat of water $=4200\mathrm{J}{\mathrm{k}\mathrm{g}}^{-1}{\mathrm{K}}^{-1}$ ${}^{}{}^{}$ and the latent heat of ice $=3.4*{10}^5\mathrm{J}{\mathrm{k}\mathrm{g}}^{-1}$ ${}^{}{}^{}$ . 100 grams of ice at $0^{?}\mathrm{C}$ ${}^{}$ is placed in $200\mathrm{g}$ $$ of water at ${25}^{?}\mathrm{C}$ ${}^{}$ . The amount of ice that will melt as the temperature of water reaches $0^{?}\mathrm{C}$ ${}^{}$ is close to (in grams):

A metallic sphere cools from ${50}^{\circ }\mathrm{C}$ to ${40}^{\circ }$  in 300 s. If atmospheric temperature around is ${20}^{\circ }\mathrm{C}$   , then the sphere's temperature after the next 5 minutes will be close to: