One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is $$100\,K$$ and the universal gas constant $$R=8.0$$ $$J\,mo{l^{ - 1}}{K^{ - 1}},$$ the decrease in its internal energy, in Joule, is ____________.

A metal is heated in a furnace where a sensor is kept above the metal surface to read the power radiated (P) by the metal. The sensor has a scale that displays $${\log _2}\left( {{P \over {{P_0}}}} \right)$$, where P₀ is a constant. When the metal surface is at a temperature of 487^oC, the sensor shows a value 1. Assume that the emissivity of the metallic surface remains constant. What is the value displayed by the sensor when the temperature of the metal surface is raised to 2767^oC?

Two spherical stars A and B emit blackbody radiation. The radius of A is 400 times that of B and A emits 10⁴ times the power emitted from B. The ratio $$\left( {{{{\lambda _A}} \over {{\lambda _B}}}} \right)$$ of their wavelengths $${{\lambda _A}}$$ and $${{\lambda _B}}$$ at which the peaks occur in their respective radiation curves is

A thermodynamic system is taken from an initial state i with internal energy U_i = 100 J to the final state f along two different paths iaf and ibf, as schematically shown in the figure. The work done by the system along the paths af, ib and bf are W_af = 200 J, W_ib = 50 J and W_bf = 100 J respectively. The heat supplied to the system along the path iaf, ib and bf are Q_iaf, Q_ib and Q_bf respectively. If the internal energy of the system in the state b is U_b = 200 J and Q_iaf = 500 J, the ratio Q_bf / Q_ib is