One mole of an ideal gas at 300 K is compressed isothermally from a volume of \(V_1\) to \(V_2\). Calculate: The work done on the gasThe change in internal energyThe heat exchanged with the surroundingsUse \(R = 8.314\, \text{J/molK}\), \( \ln(2.5) = 0.916\)
A test tube of mass 8 g and uniform cross-sectional area 12 cm2 is floating vertically in water. It contains 12 g of lead at the bottom. When the tube is slightly depressed and released, it performs vertical oscillations.Find the time period of oscillation.
Two light waves of intensities \(I_1 = 4I\) and \(I_2 = I\) interfere. If the path difference between the waves is 25 % of the wavelength \(\lambda\), find the resultant intensity at that point.
In a nuclear reactor, fuel is consumed at the rate of \(2 \times 10^{-3}\) g/s. If 100 % of the mass is converted to energy, find the power output of the reactor in kilowatts (kW).