For a closed thermodynamic system of constant composition, specify the natural variables of the following state functions and write down an equation for the complete differential of the state function with respect to the natural variables. (i) internal energy u. enthalpy h. helmholtz free energy f. [1 mark] [1 mark] [1 mark] (iii) (b) using the first and second laws of thermodynamics, the equations from part (a), equations relating enthalpy and, separately, helmholtz free energy to internal energy and the maxwell relation for helmholtz free energy, derive an expression for the partial derivative of enthalpy with respect to volume at constant temperature in terms of temperature, volume and pressure. [5 marks] using the result from part (b), explain which physical properties of a pure substance should be measured to calculate the change in enthalpy with a change in volume at constant temperature.

Calculate the kinetic energy of earth due to its spinning about its axis. krot = j compare your answer with the kinetic energy of the orbital motion of earth's center of mass about the sun. assume earth to be a homogeneous sphere of mass 6.00 1024 kg and radius 6.40 106 m. the radius of earth's orbit is 1.50 1011 m.

The us government wants to allocate billions of dollars in the next 10 years to assure our future energy security. the funds will be spread among a variety of possible energy resources. where do you think the government should put the greatest support: solar energy, wind energy, clean coal, oil exploration, gas exploration, or a combination of sources? are there other efforts that should be explored? support your position with cited information for both questions.

Fft review: linspace, fs, fftshift, nfft 1. generate one second of a cosine of w,-10hz sampled at f, = 100hz and assign it to x. define a tt as your time axis 2. take 64 points fft. 3. as you remember, the dft (which the fft implements) computes n samples of s2t where k-0,1,2, n -1. plot the magnitude of this 64-points fft at range 0 to 63, what do you think of this graph? 4â·to get the x-axis into a hz-frequency form, plot this 64-points fft between-50 to 50 (the 100hz sampling rate) and have n-points between them. 5. according to your figure, what frequency is this cosine wave at? 6. remember that the fft is evaluating from 0 to 2ď€. we are used to viewing graphs from-ď€ to ď€. therefore, you need to shift your graph. 7. now according to your shifted graph. what frequency is this at? 8. note that the spikes have long drop-offs? try a 1024-point dft. note that the peak is closer to 10 and the drop-off is quicker. although, now sidelobes are an issue