An ideal gas with adiabatic exponent $\gamma$ is heated at constant pressure. It absorbs $Q$ amount of heat. Determine the fractions of heat absorbed in raising the internal energy and performing the work.

One mole of an ideal monatomic gas undergoes the process $P=\alpha T^{1/2}$, where $\alpha$ is a constant.

Find the work done by the gas if its temperature increases by $50 \mathrm{K}$.

One mole of an ideal monatomic gas undergoes the process $P=\alpha T^{1/2}$, where $\alpha$ is a constant.

Also, find the molar specific heat of the gas.

An ideal gas is kept in closed vessel of volume $0.0083{ \mathrm{m}}^3$, at a temperature of $300 \mathrm{K}$ and a pressure of $1.6\times {10}^6 \mathrm{N}/{\mathrm{m}}^2$. An amount of $2.49\times {10}^4$ joule of heat energy is supplied to the gas. Calculate the final temperature and pressure of the gas.

(Given: The specific heat at constant pressure $C_p=5R/2$ and gas constant $R=8.3 \mathrm{J}/\mathrm{mol}-\mathrm{K}$ )

A monoatomic ideal gas is taken in a cylinder. It undergoes through the process $ABC$ as shown in figure. If the temperature at the point $A$ is $300 \mathrm{K}$ Find

(i) the temperature at points $B$ and $C$.

(Use gas constant $R=\frac{25}{3} \mathrm{J}/\mathrm{mol}-\mathrm{K}$)

A monoatomic ideal gas is taken in a cylinder. It undergoes through the process $ABC$ as shown in figure. If the temperature at the point $A$ is $300 \mathrm{K}$ Find

the work done and heat supplied to the gas in paths $AB$ and $BC$

(Use gas constant $R=\frac{25}{3} \mathrm{J}/\mathrm{mol}-\mathrm{K}$)