Hyperloop: Air compression

We know that Specific heat capacity= $\frac{Energy}{Mass*Change In Temperature}$ So now, Energy= $Specific heat capacity \times Mass\times Change In Temperature$ = $1000 \times 1.43\times 564$ =806520J So the answer is 806520J Watts

This is a little bit of a trick question, it is only the change in temperature that determines the heat capacity (not the pressure per se)

$1000 \frac{J}{kg\cdot K} * 1.43kg/s * (857-293)K = 806520 J/s$

We know that $q = mc\Delta T$ . Each second, the mass of air is 1.43 kg and the temperature change is $857 - 293 = 564 K$ , so $q = (1.43)(1000)(564) \approx 8.065*10^5 J$ . Thus the rate of heat energy gain is $\boxed{8.065*10^5 W}$ .

First of all, the pressures given (99 Pa and 2.1 kPa) are irrelevant, since the temperature change is given. We may disregard them.

More to the point, the problem asks for an answer in units of Watts, or joules per second (J/s). We may do this using dimensional analysis, canceling out unneeded units:

If we to multiply the specific heat of 1000 J/(kg * K) by 1.43 kg/s, we get 1430 J/(s * K) as the kg cancels. To cancel out K, we multiply by the temperature change during compression: 857 - 293 = 564 K. The final heat transfer rate is thus 806520 J/s, or W .