NEET UG 2004 — Thermodynamics

One mole of an ideal gas at an initial temperature of $T~ K$ does $6~ R$ joules of work adiabatically. If the ratio of specific heats of this gas at constant pressure and at constant volume is $5 / 3$, the final temperature of gas will be:

The equation of state for $5 \mathrm{~g}$ of oxygen at a pressure $P$ and temperature $T$, when occupying a volume $V$, will be: (where $R$ is the gas constant)

If $\lambda_m$ denotes the wavelength at which the radioactive emission from a black body at a temperature $T K$ is maximum, then: