In an isochoric process, the volume of the gas remains constant. Since work done is given by: \[ W = P \Delta V \] where \( \Delta V \) is the change in volume, if there is no change in volume (\( \Delta V = 0 \)), the work done by the gas is zero.
Thus, the correct answer is (C).
The ratio of the fundamental vibrational frequencies \( \left( \nu_{^{13}C^{16}O} / \nu_{^{12}C^{16}O} \right) \) of two diatomic molecules \( ^{13}C^{16}O \) and \( ^{12}C^{16}O \), considering their force constants to be the same, is ___________ (rounded off to two decimal places).}
A heat pump, operating in reversed Carnot cycle, maintains a steady air temperature of 300 K inside an auditorium. The heat pump receives heat from the ambient air. The ambient air temperature is 280 K. Heat loss from the auditorium is 15 kW. The power consumption of the heat pump is _________ kW (rounded off to 2 decimal places).
Let \( I = \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{\tan^2 x}{1+5^x} \, dx \). Then: