Physics Thermodynamics

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:

A calorimeter of water equivalent $20\mathrm{g}$  contains $180\mathrm{g}$ of water at ${25}^{?}\mathrm{C}$ , ' $\mathrm{m}$  ' grams of steam at   ${100}^{?}\mathrm{C}$ is mixed in it till the temperature of the mixture is ${31}^{?}\mathrm{C}$   . The value of

Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area 0.5 m². It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is : (g = 10 m/s²)

A balloon filled with helium (32°C and 1.7 atm.) bursts. Immediately afterwards the expansion of helium can be considered as:

Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature T is: